[" 5.Th.The "(cos x+sin x)=sqrt(2)cos x" हो,"pi(cos x-sin x)=?],[[" (a) "-sqrt(2)cos x," (b) "sqrt(2)sin x," (c) "(1)/(sqrt(2))sec x," (a) "]]

If cos x+sin x=sqrt(2)cos x, prove that that cos x-sin x=sqrt(2)sin x

cos x-sin x = sqrt (2) cos (x + (pi) / (4))

sin x + cos x = sqrt (2) cos A

2tan2x = (cos x + sin x) / (cos x-sin x) - (cos x-sin x) / (cos x + sin x)

sqrt(cos 2x) + sqrt(1 + sin 2x) = 2sqrt(sin x + cos x) if

f (x) = cos ((pi) / (sqrt (3)) sin x + sqrt ((2) / (3)) pi cos x)

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

int_(0)^(pi//2) sqrt(sin x)/(sqrt(sin x ) + sqrt( cos x)) dx =

Prove that (i) "cos " ((pi)/(3) +x) =(1)/(2) ( " cos " x - sqrt(3) sin x) (ii) " sin " ((pi)/(4) + x) + " sin " ((pi)/(4)-x) =sqrt(2) " cos " x (iii) (1)/(sqrt(2)) " cos ((pi)/(4) + x) = (1)/(2) " (cos x - sin x) " (iv) " cos x + cos " ((2pi)/(3) +x) + " cos " ((2pi)/(3)-x) =0