" 15."y=sin(x^(x))

" (y) "y=(sin x)^(x)+sin sqrt(x)

if y = sin x ^ (sin x ^ (sin x))

Show that sin(x+y)sin(x-y)= sin^2 x -sin^2 y .Hence prove that sin(x+y)sin(x-y)+sin(y+z)sin(y-z) +sin(z+x)sin(z-x)=0

If x = tan 15^(@), y = cosec 75^(@) " and " z =4 sin 18^(@), then

If y=(sin x) ^(sin x ^sin x ....oo) then prove that dy/dx=(y^2 cot x)/(1-y log (sin x))

If y=(sin x) ^(sin x ^sin x ....oo) then prove that dy/dx=(y^2 cot x)/(1-y log (sin 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)

{ xcos ((y)/(x)) + y sin ((y)/(x))} y dx = { y sin ((y)/(x)) - x cos ((y)/(x))}x dy