`(cos x)^(y)=(cos 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-

Prove that (sin x-sin y)/(cos x+cos y)=tan ((x-y)/2) .

If cos (x-y)=3 * cos (x+y) , " then " cot x* cot y=

If(cos(x-y))/(cos(x+y)=(m)/(n))8. If cos(X-Y=m then write the value of tan x tan y.

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

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

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)

The solution of equation x(dy)/(dx)cos((y)/(x))=y cos((y)/(x))-x

Prove that, cos 4 x - cos4 y = 8(cos x - cos y)(cos x + cos y)(cos x - sin x)(cos x + sin y)