Prove that : tan^-1((cosx)/(1+sinx)) = pi/4 - x/2, x in (-pi/2,pi/2)

sin^-1 (cosx) = pi/2 - x is valid for

The possible values of theta in (0,pi) such that sin (theta) + sin (4theta) + sin(7theta) = 0 are (1) (2pi)/9 , i/4 , (4pi)/9, pi/2, (3pi)/4 , (8pi)/9 (2) pi/4, (5pi)/12, pi/2 , (2pi)/3, (3pi)/4, (8pi)/9 (3) (2pi)/9, pi/4 , pi/2 , (2pi)/3 , (3pi)/4 , (35pi)/36 (4) (2pi)/9, pi/4, pi/2 , (2pi)/3 , (3pi)/4 , (8pi)/9

sin^(-1)(sin""(3pi)/5)=(2pi)/5 .

Prove that cos^-1 ((sin x + cos x )/(sqrt2)) = x - (pi/4), (pi/4) le x le ((5pi)/4)

Differentiate (sin x - cos x)^(sin x -cos x) , (-pi)/(4) lt x lt (3pi)/4

If f'(x) = a sin x + b cos x and f'(0) = 4,f(0) = 3, f((pi)/(2))= 5 , find f(x).

Prove that sin^(-1)""(3)/(5)+sin^(-1)""(4)/(5)=(pi)/(2)

Prove that cos^(-1)""(3)/(5)+cos^(-1)""(4)/(5)=(pi)/(2)

Solve |sqrt(3) cos x - sin x |ge 2 for x in [0,4pi] .