" 21."tan^(2)((pi x^(2))/(2))

if y=tan^(2)((pi x^(2))/(2)), prove that (dy)/(dx)=2 pi x tan((pi x^(2))/(2))sec^(2)((pi x^(2))/(2))

int ["tan"(x)/(2)+"tan" ((pi)/(2)-(x)/(2))]dx=

int _ (-2)^(1) (tan^(-1) ((x)/(x^(2) +1))+tan^(-1) ((x^(2) +1)/( x))) dx is (i) (pi)/(2) (ii)-(pi)/(2) (iii) pi (iv) -pi

tan^(2)((pi)/(16))+tan^(2)((2 pi)/(16))+tan^(2)((3 pi)/(16))... ..+tan^(2)((7 pi)/(16)/)=35

Maximum value of y = (1-tan ^ (2) ((pi) / (4) -x)) / (1 + tan ^ (2) ((pi) / (4) -x))

lim_(x to pi/2) (tan2x)/(x-(pi)/(2))

(sec2x-tan2x) equals a tan(x-(pi)/(4))b)tan((pi)/(4)-x)c cot(x-(pi)/(4))d tan^(2)(x+(pi)/(4))

Provet that " tan " ((pi)/(4) +(x)/(2)) + " tan " ((pi)/(4)-(x)/(2)) = " 2 sec x"

Number of solutions of the trigonometric equation cos^(2)((pi)/(4)(cos x+sin x))-tan^(2)(x+(pi)/(4)tan^(2)x)=1in[-2 pi,2 pi] is

If 0 lt x lt (pi)/(4), then sec 2x - tan 2x= ................ A) tan (x- (pi)/(4)) B) tan ((pi)/(4) -x) C) tan (x+(pi)/(4)) D) tan ^(2) (x+ (pi)/(4))