If `0 lt alpha lt beta lt (pi)/(2)`, prove that, `tan alpha-tan beta lt alpha-beta`.

Prove that |cosalpha-cosbeta|lt=|alpha-beta|

if 0ltalpha,beta,gamma lt(pi/2) prove that sin alpha+sin beta+sin gamma gtsin(alpha+beta+gamma)

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

If cos (theta - alpha) = a and sin(theta - beta) = b (0 lt theta - alpha, theta - beta lt pi//2) , then prove that cos^(2) (alpha - beta) + 2ab sin (alpha - beta) = a^(2) + b^(2)

Suppose alpha,beta a n d theta are angles satisfying 0 < alpha < theta < beta < pi/2 dot Then prove that (sin alpha-sin beta)/(cos beta-cos alpha)=-cot theta

Find the values of alpha and beta[ 0 lt alpha, beta lt (pi)/(2)] satisfying the equation cos alpha cos beta cos (alpha+ beta)=-(1)/(8)

If alpha+ beta=(pi)/(2) and beta+ gamma= alpha then prove that tan alpha=tan beta+2 tan gamma .

If sin 2 alpha = 4 sin 2 beta, "show that", 5tan ( alpha -beta) = 3 tan ( alpha +beta)

If alpha + beta =(pi)/(2)and beta + gamma =alpha, then the value of tan alpha is -

Let alpha,beta,gamma>0a n dalpha+beta+gamma=pi/2dot Then prove that sqrt(tanalphatanbeta) + sqrt(t a nbeta"tan"gamma)+sqrt(tanalphatangamma)lt=sqrt(3)