Differentiate with respect to x:
sin inverse(a+bcosx/b+acosx)

Share with your friends

Share 9

Question

Differentiate with respect to x:
sin inverse(a+bcosx/b+acosx)

Rishabh Mittal · Accepted Answer

Dear Student ,

Please find below the solution to the asked query :

Let y=sin-1 a+ b cos xb+a cos xsin y=a+ b cos xb+a cos xDifferentiating wrt x on both sides, we getcos y dydx=0-b sin x b+a cos x - a+b cos x 0-a sin xb+a cos x2cos y dydx=-b2 sin x -ab sin x cos x+a2 sin x+ab sin x cos xb+a cos x21-sin2y dydx=-b2 sin x +a2 sin xb+a cos x2dydx=a2-b2 sin xb+a cos x2
11-sin2y=a2-b2 sin xb+a cos x2
11-sinsin-1 a+ b cos xb+a cos x2=a2-b2 sin xb+a cos x2
11-a+ b cos xb+a cos x2=a2-b2 sin xb+a cos x2
b+a cos xb+a cos x2-a+b cos x2=a2-b2 sin xb+a cos x
1b2+a2 cos2x +2ab cos x-a2-b2 cos2x-2ab cos x=a2-b2 sin xb+a cos x
1b2+a2 cos2x -a2-b2 cos2x=a2-b2 sin xb+a cos x
1-cos2x b2-a2+1 b2-a2=-b2-a2 sin xb+a cos x
1b2-a2 1-cos2x=- b2-a2b+ a cos x     ANS
Hope this information will clear your doubts about the topic
If you have any more doubts just ask here on the forum and our
experts will try to help you out as soon as possible

Regards

Differentiate with respect to x: sin inverse(a+bcosx/b+acosx)

Differentiate with respect to x:
sin inverse(a+bcosx/b+acosx)