# Overiť totožnosť. 1-sinx cosx = cosx 1 + sinx

Dec 06, 2019 · Ex 7.5, 17 cos﷮𝑥﷯﷮(1− sin﷮𝑥﷯)(2 − sin﷮𝑥)﷯﷯ [Hint: Put sin x = t]Let sin﷮𝑥﷯=𝑡Diff. 𝑤.𝑟.𝑡.𝑥 𝑐𝑜𝑠﷮𝑥﷯= 𝑑𝑡﷮𝑑𝑥﷯ 𝑑𝑥= 𝑑𝑡﷮ 𝑐𝑜𝑠﷮𝑥﷯﷯Now we can write ﷮﷮ cos﷮𝑥﷯﷮(1− sin﷮𝑥﷯)(2 − sin﷮𝑥)﷯﷯﷯𝑑𝑥= ﷮﷮ cos﷮𝑥﷯﷮(1 − 𝑡)(2 − 𝑡) ﷯﷯ 𝑑𝑡

multiply the LHS , top and bottom by (1+sinx) ((1-sinx)(1+sinx))/(cosx(1+sinx)) = (1-sin^2x)/(cosx(1+sinx)) but sin^2x+cos^x=1 :. =(cos^2x)/(cosx(1+sinx)) =(cancel(cosx)(cosx))/(cancelcosx(1+sinx)) as required. About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features Press Copyright Contact us Creators Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. Prove that Cosx/(1-Sinx) = (1+Cosx+Sinx)/(1+Cosx-Sinx) i) Grouping the given one, it is: { (1 - cosx) + sinx}/ { (1 + cosx) + sinx} ii) By multiple/sub multiple angle identities, 1 - cosx = 2*sin² (x/2); 1 + cosx = 2*cos² (x/2) and sin (x) = 2*sin (x/2)*cos (x/2) iii) Substituting these in (i) above, Left side = {2*sin² (x/2) + 2*sin (x/2)*cos (x/2)}/ {2*cos² (x/2) + 2*sin (x/2)*cos (x/2)} 1/ sinx(1 + cosx) = 1 + cosx + cos^2x 2/ sin^3x + cos^3x = sinx - cosx 3/ 3 cos^4x -4 sin^2xcos^2x + sin^4x = 0 Đăng chủ đề mới Cộng đồng học sinh Việt Nam - HOCMAI Forum Trigonometry Formula List: https://www.youtube.com/watch?v=EaSV-VasbnQ&list=PLJ-ma5dJyAqqEv5UpYmUFj6PVyMpHrLZ6&index=1 Get an answer for 'Verify: (cosx/1 + sinx) + (cosx/1-sinx) = 2secx' and find homework help for other Math questions at eNotes We’ve discounted annual subscriptions by 50% for COVID-19 relief Solve your math problems using our free math solver with step-by-step solutions. Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more. In order to prove the trigonometric identity, we need to start with one side and use known identities to get to the other side: LS={1-sinx}/cosx multiply by 1+sinx in numerator and denominator Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Feb 13, 2020 · Transcript. Misc 9 Find sin /2, cos /2 and tan /2 for cos = 1/3 , in quadrant III Since x is in quadrant III 180 < x < 270 Dividing by 2 all sides (180 )/2 < /2 < (270 )/2 90 < /2 < 135 So, /2 lies in IInd quadrant In IInd quadrant, sin is positive, cos & tan are negative sin /2 Positive and cos /2 and tan /2 negative Given, cos x = 1/3 cos x = 2 cos2 /2 1 1/3 = 2cos2 /2 1 1 1/3 = 2cos2 /2 (3 ?(x+sinx)/(1+cosx)dx = Find the answer to this question along with unlimited Maths questions and prepare better for JEE 2020 exam. Dec 20, 2019 · Ex 7.3, 14 Integrate the function cos⁡〖𝑥 − sin⁡𝑥 〗/(1 + sin⁡2𝑥 ) ∫1 cos⁡〖𝑥 − sin⁡𝑥 〗/(1 + sin⁡2𝑥 ) 𝑑𝑥 =∫1 cos⁡〖𝑥 −〖 sin〗⁡𝑥 〗/(𝟏 + 2 sin⁡𝑥 cos⁡𝑥 ) 𝑑𝑥 =∫1 cos⁡〖𝑥 −〖 sin〗⁡𝑥 〗/(〖𝐬𝐢𝐧〗^𝟐⁡𝒙 + 〖𝐜𝐨𝐬〗^𝟐⁡𝒙 + 2 sin⁡cos⁡𝑥 ) 𝑑𝑥 =∫1 cos Oct 14, 2007 · (sin x + cos x)/(sin x - cos x) = (1 + 2 sin x cos x)/(2 sin² x - 1) LRS = (sin x + cos x)/(sin x - cos x) = We can multiply it by (sin x + cos x)/(sin x + cos x), since it's equal to 1: (sin x + cos x)/(sin x - cos x) ∙ (sin x + cos x)/(sin x + cos x) = We'll get a Newton's binomial on the numerator, a difference between squares on the denominator: (sin x + cos x)²/(sin² x - cos² x 1 + sinx = sin^2(x/2) +cos^2((x/2) + 2sin(x/2)*cos(x/2) ={sin(x/2) +cos(x/2)}^2 Similarly, 1-sinx = sin^2(x/2)+cos^2(x/2) - 2sin(x/2)*cos(x/2) ={sin(x/2)- cos(x/2)}^2 Apr 29, 2010 · Since 1 ≥ (sinx, cosx) ≥ 0 in the interval, sinx ≥ sin 2 x and cosx ≥ cos 2 x. Therefore sinx + cosx ≥ sin 2 x + cos 2 x = 1.

## Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history Dec 07, 2007 · 1. ( secx/sinx) - (sinx/cosx) = ( 1 / sin x cos x) - ( sinx / cos x) = ( 1 - sin^2 x)/ (sin x cos x) = cos^2 x / (sin x cos x) = cos x / sin x = cot x ans. 2.

### Prove that Cosx/(1-Sinx) = (1+Cosx+Sinx)/(1+Cosx-Sinx)

( secx/sinx) - (sinx/cosx) = ( 1 / sin x cos x) - ( sinx / cos x) = ( 1 - sin^2 x)/ (sin x cos x) = cos^2 x / (sin x cos x) = cos x / sin x = cot x ans. 2. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. 0 0. Anonymous.

Dec 31, 2012 Aug 31, 2016 overiť, či sú splnené všetky predpoklady uvedené vo vete! 1. I.Vypočítajtelimitu: 1 x − 1 ex−1 23. limx→0 1 sinx e−x(cosx+sinx) 42. limx→∞ 1++sin cos ( x+sin cos )esinx 2.

A much simpler way to find the answer is to observe graphically that the line x + y = -1 crosses the unit circle at (-1,0) and (0,-1) and therefore sin t + cos t = 1 Prove 1-(Sin(x)-cos(x))^{2}=sin(2x) en. Related Symbolab blog posts. High School Math Solutions – Trigonometry Calculator, Trig Identities. Feb 13, 2020 · Transcript. Misc 9 Find sin /2, cos /2 and tan /2 for cos = 1/3 , in quadrant III Since x is in quadrant III 180 < x < 270 Dividing by 2 all sides (180 )/2 < /2 < (270 )/2 90 < /2 < 135 So, /2 lies in IInd quadrant In IInd quadrant, sin is positive, cos & tan are negative sin /2 Positive and cos /2 and tan /2 negative Given, cos x = 1/3 cos x = 2 cos2 /2 1 1/3 = 2cos2 /2 1 1 1/3 = 2cos2 /2 (3 ?(x+sinx)/(1+cosx)dx = Find the answer to this question along with unlimited Maths questions and prepare better for JEE 2020 exam. Dec 20, 2019 · Ex 7.3, 14 Integrate the function cos⁡〖𝑥 − sin⁡𝑥 〗/(1 + sin⁡2𝑥 ) ∫1 cos⁡〖𝑥 − sin⁡𝑥 〗/(1 + sin⁡2𝑥 ) 𝑑𝑥 =∫1 cos⁡〖𝑥 −〖 sin〗⁡𝑥 〗/(𝟏 + 2 sin⁡𝑥 cos⁡𝑥 ) 𝑑𝑥 =∫1 cos⁡〖𝑥 −〖 sin〗⁡𝑥 〗/(〖𝐬𝐢𝐧〗^𝟐⁡𝒙 + 〖𝐜𝐨𝐬〗^𝟐⁡𝒙 + 2 sin⁡cos⁡𝑥 ) 𝑑𝑥 =∫1 cos Oct 14, 2007 · (sin x + cos x)/(sin x - cos x) = (1 + 2 sin x cos x)/(2 sin² x - 1) LRS = (sin x + cos x)/(sin x - cos x) = We can multiply it by (sin x + cos x)/(sin x + cos x), since it's equal to 1: (sin x + cos x)/(sin x - cos x) ∙ (sin x + cos x)/(sin x + cos x) = We'll get a Newton's binomial on the numerator, a difference between squares on the denominator: (sin x + cos x)²/(sin² x - cos² x 1 + sinx = sin^2(x/2) +cos^2((x/2) + 2sin(x/2)*cos(x/2) ={sin(x/2) +cos(x/2)}^2 Similarly, 1-sinx = sin^2(x/2)+cos^2(x/2) - 2sin(x/2)*cos(x/2) ={sin(x/2)- cos(x/2)}^2 Apr 29, 2010 · Since 1 ≥ (sinx, cosx) ≥ 0 in the interval, sinx ≥ sin 2 x and cosx ≥ cos 2 x. Therefore sinx + cosx ≥ sin 2 x + cos 2 x = 1. By multiplying both numerator and denominator by 1+sinx and using the difference of squares the result follows quickly. multiply the LHS , top and bottom by (1+sinx) ((1-sinx)(1+sinx))/(cosx(1+sinx)) = (1-sin^2x)/(cosx(1+sinx)) but sin^2x+cos^x=1 :. =(cos^2x)/(cosx(1+sinx)) =(cancel(cosx)(cosx))/(cancelcosx(1+sinx)) as required. About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features Press Copyright Contact us Creators Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. Prove that Cosx/(1-Sinx) = (1+Cosx+Sinx)/(1+Cosx-Sinx) i) Grouping the given one, it is: { (1 - cosx) + sinx}/ { (1 + cosx) + sinx} ii) By multiple/sub multiple angle identities, 1 - cosx = 2*sin² (x/2); 1 + cosx = 2*cos² (x/2) and sin (x) = 2*sin (x/2)*cos (x/2) iii) Substituting these in (i) above, Left side = {2*sin² (x/2) + 2*sin (x/2)*cos (x/2)}/ {2*cos² (x/2) + 2*sin (x/2)*cos (x/2)} 1/ sinx(1 + cosx) = 1 + cosx + cos^2x 2/ sin^3x + cos^3x = sinx - cosx 3/ 3 cos^4x -4 sin^2xcos^2x + sin^4x = 0 Đăng chủ đề mới Cộng đồng học sinh Việt Nam - HOCMAI Forum Trigonometry Formula List: https://www.youtube.com/watch?v=EaSV-VasbnQ&list=PLJ-ma5dJyAqqEv5UpYmUFj6PVyMpHrLZ6&index=1 Get an answer for 'Verify: (cosx/1 + sinx) + (cosx/1-sinx) = 2secx' and find homework help for other Math questions at eNotes We’ve discounted annual subscriptions by 50% for COVID-19 relief Solve your math problems using our free math solver with step-by-step solutions. Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more. In order to prove the trigonometric identity, we need to start with one side and use known identities to get to the other side: LS={1-sinx}/cosx multiply by 1+sinx in numerator and denominator Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.