If vector ` vec b=(t a nalpha,-1, 2sqrt(sinalpha//2))a n d vec c=(t a nalpha, t a nalpha, 3/(sqrt(sinalpha//2)))` are orthogonal and vector ` vec a=(1,3,sin2alpha)` makes an obtuse angle with the z-axis, then the value of `alpha` is a`alpha=tan^(-1)2` b. `alpha=-tan^(-1)2` c. `alpha=tan^(-1)2` d. `alpha=tan^(-1)2`

If vector vec b=(t a nalpha,-12sqrt(sinalpha//2))a n d vec c=(t a nalpha, t a nalpha-3/(sqrt(sinalpha//2))) are orthogonal and vector vec a=(13,sin2alpha) makes an obtuse angle with the z-axis, then the value of alpha is alpha=(4n+1)pi+tan^(-1)2 b. alpha=(4n+1)pi-tan^(-1)2 c. alpha=(4n+2)pi+tan^(-1)2 d. alpha=(4n+2)pi-tan^(-1)2

If alpha=pi/(14), then the value of (tanalphatan2alpha+tan2alphatan4alpha+tan4alphatanalpha) is 1 (b) 1//2 (c) 2 (d) 1//3

If alpha in (-(pi)/(2), 0) , then find the value of tan^(-1) (cot alpha) - cot^(-1) (tan alpha)

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

Prove that sin 4alpha = 4 tan alpha (1 - tan^(2) alpha)/((1 + tan^(2) alpha)^(2))

If alpha and beta (alpha gt beta) are the roots of x^(2) + kx - 1 =0 , then find the value of tan^(-1) alpha - tan^(-1) beta

The value of (sin(pi-alpha))/(sin alpha-cos alpha tan.(alpha)/(2))-cos alpha is

Prove that sin4 alpha=4tan alpha (1- tan^(2)alpha)/((1+tan^2 alpha)^2

If sin theta = 3 sin ( theta + 2 alpha) , then the value of tan (theta + alpha ) + 2 tan alpha is