Question 4. If y = cos - '(1-x'), 0

If y=y(x) is the solution of the equation e^(sin y) cos y""(dy)/(dx) +e^(sin y) cos x = cos x,y (0)=0, then 1+y ((pi)/(6)) +( sqrt(3))/(2) y((pi)/(3)) +(1)/( sqrt(2)) y((pi)/(4)) is equal to

If (cos ^ (4) x) / (cos ^ (2) y) + (sin ^ (4) x) / (sin ^ (2) y) = 1 then prove that (cos ^ (4) y) / (cos ^ (2) x) + (sin ^ (4) y) / (sin ^ (2) x) = 1

I : If cos x + cos y=1/3 , sin x+sin y=1//4 " then " cos (x+y)=7//25 II : If cos x + cos y=1//3 , sin x + sin y=1//4 " then " sin(x+y)=24//25

lim_(x to 0) (1 - cos 4x)/(1 - cos x) = _________

Prove that (i) cos (n + 2) x cos (n+1) x +sin (n+2) x sin (n+1) x = cos x) (ii) " cos " .((pi)/(4)-x) " cos " .((pi)/(4)-y) " - sin " ((pi)/(4)-x ) " sin " ((pi)/(4) -y) =" sin " (x+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)

The area of the closed figure bounded by y=1 //cos^(2)x,x=0,y=0and x=pi//4, is