If `2cosbeta = cos (2alpha +beta)` then `3 tan (alpha+beta) + cotalpha` is independent of-

If 2cos beta=co(2 alpha+beta) then 3tan(alpha-beta)+cos alpha is independent of

If 3sin beta=sin(2 alpha+beta) then tan(alpha+beta)-2tan alpha is (a)independent of alpha (bindependent of beta (c)dependent of both alpha and beta( d)independent of both alpha and beta

If 3sinbeta=sin(2alpha+beta) then tan(alpha+beta)-2tanalpha is (a)independent of alpha (b)independent of beta (c)dependent of both alpha and beta (d)independent of both alpha and beta

If 3sinbeta=sin(2alpha+beta) then tan(alpha+beta)-2tanalpha is (a)independent of alpha (b)independent of beta (c)dependent of both alpha and beta (d)independent of both alpha and beta

If 3sinbeta=sin(2alpha+beta) then tan(alpha+beta)-2tanalpha is (a)independent of alpha (b)independent of beta (c)dependent of both alpha and beta (d)independent of both alpha and beta

Prove that sin^(2)alpha + cos^(2) (alpha + beta) + 2 sin alpha sin beta cos (alpha + beta) is independent of alpha .

The expression (tan alpha+tan beta)cot(alpha+beta)+(tan alpha-tan beta)cot(alpha-beta) is independent of both alpha and beta.

Prove that cos^(2)(alpha-beta)+cos^(2)beta-2cos(alpha-beta)cosalphacosbeta is independent of beta .

The expression cos^(2)(alpha + beta + gamma) + cos^(2)(beta + gamma) + cos^(2)alpha - 2cos alpha cos(beta + gamma)cos(alpha + beta + gamma) is (a) independent of alpha (b) independent of beta (c) dependent on gamma only (d) dependent on alpha, beta, gamma