Evaluate : `cos^2 (pi/4 + x) - sin^2 (pi/4 -x)`

cos((3pi)/4+x)-sin(pi/4-x)=?

Evaluate lim_(x to (pi)/(4)) (cos x - "sin" x)/(cos 2x)

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)

(cos ^ (2) ((pi) / (4) -A) -sin ^ (2) ((pi) / (4) -A)) / (cos ^ (2) ((pi) / (4) + A) + sin ^ (2) ((pi) / (4) + A) =)

Evaluate : int_0^(pi/4) ( cos 2 x)/( cos 2x + sin 2x) dx

Evaluate int _(-pi//2)^(pi//4) sin ^(2) x dx .

Evaluate int_0^(pi/4) dx/(cos^2x + 4sin^2x)

Evaluate: int_0^(pi/2) (sin2x)/(sin^4x+cos^4x)dx

Evaluate: int_(-pi/4)^( pi/4)(x+pi/4)/(2-cos2x)dx

Let Q = [{: (cos ""(pi)/(4) , - sin""(pi)/(4)),(sin""(pi)/(4), cos""(pi)/(4)):}] and x = [{:((2)/(sqrt(2))),((1)/(sqrt(2))):}] then Q^(3) x is equal to