(cos x)^(y)=(sin y)^(x)

If tan(7x^(@))=(sin x^(@)cos y^(@)+cos x^(@)sin y^(@))/(cos x^(@)cos y^(@)-sin x^(@)sin^(@)) where x+y=134^(@) ,then the least positive integral value of x, is-

Draw the graph of following function y = cos ^ (- 1) (cos x) y = sin ^ (- 1) (sin x) y = cos (cos ^ (- 1) x) y = sin (sin ^ (- 1) x)

The number of pairs (x, y) of real numbers with 0 lt x lt (pi)/( 2) " that " ((sin x)^(2y))/((cos x)^((y^(2))/(2)))+((cos x)^(2y))/((sin x) ^((y^(2))/(2)))= sin 2 x is equal to

prove that: cos ^ (2) x + cos ^ (2) y-2cos x * cos y * cos (x + y) = sin ^ (2) (x + y)

[x (cos y) / (x) + y (sin y) / (x)] y = [y (sin y) / (x) -x (cos y) / (x)] x ((dy) / (dx))

Prove that : (sin (x+y))/(sin (x-y) )= (sin x. cos y + cos x . Sin y)/(sin x. cos y-cos x. sin y)

Prove that : (sin (x+y))/(sin (x-y) )= (sin x. cos y + cos x . Sin y)/(sin x. cos y-cos x. sin y)

The value of (sin x cos y + cos x sin y)^2+(cos x cos y -sin x sin y)^2 is equal to

{x cos (y/x)+y sin (y/x)} y d x={y sin (y/x)-(x) cos (y/x)} x d y

cos4x-cos4y = 8 (cos x-cos y) (cos x + cos y) (cos x-sin y) (cos x + sin y)