Expand `cos(x+y)` and hence prove
`cos2x=1-2sin^2x`

Prove that 1+cos 2x=2cos^2x .

Show that cos 2 x=cos ^(2) x-sin ^(2) x=2 cos ^(2) x-1=1-2 sin ^(2) x=(1-tan ^(2) x)/(1+tan ^(2) x)

If y=sin(m sin^-1x) , Hence prove that (1-x^2)(d^2y)/dx^2-xdy/dx+m^2y=0 .

Find the integral (cos 2 x)/(cos x+sin x)^2

If cos x + cos^(2) x =1 , then the value of sin^(4) x + sin^(6) x is

If sin (x + y) =1/2 , prove that y = sin^-1 (1/2) - x

Find the integral (cos x-sin x)/(1+sin 2 x)

Show that (i) cos x+cos y=2 cos (x+y)/(2) cos (x-y)/(2) (ii) cos x-cos y=-2 sin (x+y)/(2) sin (x-y)/(2) (iii) sin x+sin y=2 sin (dot(x)+y)/(2) cos (x-y)/(2) (iv) sin x-sin y=2 cos (x+y)/(2) sin (x-y)/(2)

Prove that (i) 2 cos x cos y=cos (x+y)+cos (x-y) (ii) -2 . sin x sin y=cos (x+y)-cos (x-y) (iii) 2 sin x cos y=sin (x+y)+sin (x-y) (iv) 2 cos x sin y=sin (x+y)-sin (x-y)