[8T],[" 14."(cos x)^(y)=(cos y)^(x)]

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

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

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)

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

If 3sin(x y)+4cos(x y)=5,t h e n(dy)/(dx)= (a) -y/x (b) (3sin(x y)+4cos(x y))/(3cos(x y)-4sin(x y)) (c) (3cos(x y)+4sin(x y))/(4cos(x y)-3sin(x y)) (d) (sin^2(a+y))/(sina)

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)

If int_(y)^(y)cos t^(2)dt=int_(0)^(x^(2))(sin t)/(t)dx, the prove that (dy)/(dx)=(2sin x^(2))/(x cos y^(2))

If x in (-pi, pi) such that y=1 +|cos x|+|cos^(2)x|+|cos^(3)|+ …. And 8^(y)=64 , then y =

What is the value of {sin (x+y) -2 sin x+ sin(x-y)} /[cos (x-y) +cos (x+ y)-2 cos x] xx [(sin 10x- sin 8x)/ (cos-10x + cos 8x)] ? {[sin (x+y] -2 sin x+ sin(x-y)}//[cos (x-y) +cos (x+ y)-2 cos x]} xx [(sin 10x-sin 8x)//(cos10x + cos 8x)] का मान क्या है?