`sin m((pi)/(2)+x)+cos n((pi)/(2)-x)`

The expression (tan(x-(pi)/(2))cos((3 pi)/(2)+x)-sin^(3)((7 pi)/(2)-x))/(cos(x-(pi)/(2))tan((3 pi)/(2)+x)) is equal to

The expression (tan(x-(pi)/(2)).cos((3pi)/(2)+x)-sin^(3)((7pi)/(2)-x))/(cos(x-(pi)/(2)).tan((3pi)/(2)+x)) simplifies to

(cos (pi + x) cos (-x)) / (sin (pi-x) cos ((pi) / (2) -x)) = cot ^ (2) x

If A(x)=det[[x^(n),sin x,cos xn!sin((n pi)/(2)),cos((n pi)/(2))a,a^(2),a^(3)]], then the value of (d^(n))/(dx^(n))[Delta(x)] at x=0 is

(sin (pi + x) cos ((pi) / (2) + x) tan ((3 pi) / (2) -x) cot (2 pi-x)) / (sin (2 pi-x) cos (2 pi + x) csc (-x) sin ((3 pi) / (2) -x)) = 1

If the expression cos(x-3(pi)/(2))+sin(3(pi)/(2)+x)+sin(32 pi+x)-18cos(19 pi-x)+cos(56 pi+x)-sin(x+17 pi) is expressed in the form of a sin x+b cos x, then a+b is equal to

The period of sin((pi x)/(2))+cos((pi x)/(3)) is

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)

[sin ((pi) / (2) -x) + sin (pi-x)] ^ (2) + [(cos ((3 pi) / (2) -x) + cos (2 pi-x)] ^ (2) =

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