`" sin " (x-(pi)/(6)) + " cos " (x-(pi)/(3)) =sqrt(3) " sin " x`

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

lim_ (x rarr (pi) / (6)) (sin (x- (pi) / (6))) / (sqrt (3) -cos x)

sin(x-pi/6)+cos(x-pi/3)=sqrt3 sinx

lim_ (x rarr (pi) / (6)) (2 (sin x cos ((pi) / (6)) - cos x sin ((pi) / (6)))) / (x- (pi) / (6))

In each of the following cases find the period of the function if it is periodic. (i) f(x)="sin"(pi x)/(sqrt(2))+"cos"(pi x)/(sqrt(3)) " (ii) " f(x)="sin"(pi x)/(sqrt(3))+"cos"(pi x)/(2sqrt(3))

If : sin(x+(pi)/(3)) = cos (x-(pi)/(6)),"then" : tan x = A) 1//sqrt3 B) -1//sqrt3 C) sqrt3 D) -sqrt3

Maximum value of sin (x + (pi)/(6)) + cos (x + (pi)/(6)) is

Prove that: cos((3 pi)/(4)+x)-cos((3 pi)/(4)-x)=-sqrt(2)sin x

Prove that: cos((3 pi)/(4)+x)-cos((3 pi)/(4)-x)=-sqrt(2)sin x

Prove that: cos((3 pi)/(4)+x)-cos((3 pi)/(4)-x)=sqrt(2)sin x