If `sin alpha = 3/5, tan beta = 1/2 and pi/2 lt alpha lt pi lt beta lt (3pi)/2`, show that `8 tan alpha - sqrt(5) sec beta = - 7/2`.

If 0 lt alpha lt beta lt (pi)/(2) then

If sin (alpha + beta) = 4/5 , cos (alpha - beta) = (12)/(13) 0 lt alpha lt (pi)/(4), 0 lt beta lt (pi)/(4), find tan 2 alpha .

If alpha = cos^(-1)((3)/(5)), beta = tan ^(-1)((1)/(3)) , where 0 lt alpha, beta lt (pi)/(2) , then alpha - beta is equal to

lf cos^2 alpha -sin^2 alpha = tan^2 beta , then show that tan^2 alpha = cos^2 beta-sin^2 beta .

If 0 lt alpha, beta lt pi and they satisfy cos alpha + cosbeta - cos(alpha + beta)=3/2

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

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)

If 3 sin alpha=5 sin beta , then (tan((alpha+beta)/2))/(tan ((alpha-beta)/2))=

If 0 lt alpha lt pi/6 , then the value of (alpha cosec alpha ) is

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