If `(1+tanalpha)(1+tan4alpha)=2,alpha in (0,pi/(16)),` then `alpha` is equal to (a)`pi/(20)` (b) `pi/(30)` (c) `pi/(40)` (d) `pi/(60)`

If n=pi/(4alpha), then tanalpha tan 2alpha tan 3 alpha........tan(2n-1)alpha is equal to

If 2|sin2alpha|=|tanbeta+cotbeta|,alpha,beta in (pi/2,pi), then the value of alpha+beta is (a) (3pi)/4 (b) pi (c) (3pi)/2 (d) (5pi)/4

If alpha in (-(3pi)/2,-pi) , then the value of tan^(-1)(cotalpha)-cot^(-1)(tanalpha)+sin^(-1)(sinalpha)+cos^(-1)(cosalpha) is equal to (a) 2pi+alpha (b) pi+alpha (c) 0 (d) pi-alpha

If 2 sin 2alpha=tan beta,alpha,beta, in((pi)/(2),pi) , then the value of alpha+beta is

If tanalpha=1/3,tanbeta=1/7 ,show that 2alpha +beta=pi/4

If alpha+beta=pi/2a n dbeta+gamma=alpha, then tanalpha equals

If 0 lt alpha lt (pi)/(3) , then prove that alpha (sec alpha) lt (2pi)/(3).

(lim)_(xrarr0)(sin(picos^2x)/(x^2)) is equal to (a) -pi (b) pi (c) pi/2 (d) 1

(sqrt2-sinalpha-cosalpha)/(sinalpha-cosalpha) is equal to (a) sec(alpha/2-pi/8) (b) cos(pi/8-alpha/2) (c) tan(alpha/2-pi/8) (d) cot(alpha/2-pi/2)