Let `alpha,beta in R` , satisfy the equations `cot^(2)alpha-cos ec^(2)beta=(2k)/(3)-5&cot^(2)beta-cos ec^(2)alpha=(k^(2))/(2)` , then product of all possible value(s) of `k` is equal to

(tan alpha+cos ec beta)^(2)-(cot beta-sec alpha)^(2)=2tan alpha cot beta(cos ec alpha+sec beta)

Let alpha , beta be two real numbers satisfying the following relations alpha^(2)+beta^(2)=5 , 3(alpha^(5)+beta^(5))=11(alpha^(3)+beta^(3)) Possible value of alpha + beta is

Let alpha and beta be two real roots of the equation 5 cot ^(2) x- 3 cot x-1=0, then cot ^(2)(alpha + beta)=

The value of 2alpha+beta(0ltalpha, beta lt (pi)/(2)) , satisfying the equation cos alpha cos beta cos (alpha+beta)=-(1)/(8) is equal to

The expression cos^(2)(alpha+beta)+cos^(2)(alpha-beta)-cos2 alpha cos2 beta is

cot^(2)alpha=1+a^(2) then cos ec alpha+cot^(3)alpha sec alpha=

cot^(2)alpha=1+a^(2) then cos ec alpha+cot^(3)alpha sec alpha=

Three positive acute angles alpha, beta and gamma satisfy the relation tan. (beta)/(2)=(1)/(3)cot.(alpha)/(2)and cot.(gamma)/(2)=(1)/(2)(3tan.(alpha)/(2)+cot.(alpha)/(2)) . Then, the value of alpha+beta+gamma is equal to

Prove that: cos2 alpha cos2 beta+sin^(2)(alpha-beta)-sin^(2)(alpha+beta)=cos2(alpha+beta)