14.(cos x)^(y)=(cos y)^(x)

If (cos x)^y = (cos y)^x then show that (dy)/(dx) = (y tan x+log cos y)/(x tan y+log cos x).

If y= (cos x)^((cos x)^((cos x)……oo)) , then show that (dy)/(dx)= (y^(2) tan x)/(y.log cos x-1)

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-

y=a cos x+b sin x+x sin x is a solution of the D.E. A) y_(2)+y=x cos x B) y_(2)+2y=2cos x C) y_(2)+y=2cos x D) y_(2)-y=2cos 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)

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