If `(alpha+beta+gamma+delta) = pi` then `sum cos alpha cos beta-sum sin alpha sin beta=`

If cos (alpha + beta) sin (gamma + delta) = cos (alpha - beta) sin (gamma - delta) then:

Find the value of, cos alpha cos beta, cos alpha sin beta, -no alpha-sin beta, cos beta, 0 sin alpha cos beta, sin alpha sin beta, cos alpha] |

Evaluate: quad =|cos alpha cos beta cos alpha sin beta-sin alpha-sin beta cos beta0sin alpha cos beta sin alpha sin beta cos alpha|

If cos (alpha - beta) + cos (beta - gamma) + cos (gamma - alpha) = (-3)/(2) then prove that cos alpha + cos beta+ cos gamma = sin alpha + sin beta + sin gamma = 0 .

(i) sin (alpha + beta) = sin alpha cos beta + cos alpha sin beta) (ii) sin (alpha-beta)= sin alpha cos beta- cos alpha sin beta Proof

cos alpha * sin (beta - gamma ) + cos beta * sin ( gamma - alpha ) + cos gamma * sin ( alpha - beta )=

Evaluate {:|( cos alpha cos beta , cos alpha sin beta , -sin alpha ),( -sin beta , cos beta, 0),( sin alpha cos beta, sin alpha sin beta, cos alpha ) |:} =0

Evaluate {:[( cos alpha cos beta , cos alpha sin beta , -sin alpha ),( -sin beta , cos beta, 0),( sin alpha cos beta, sin alpha sin beta, cos alpha ) ]:} =0

Evaluate {:[( cos alpha cos beta , cos alpha sin beta , -sin alpha ),( -sin beta , cos beta, 0),( sin alpha cos beta, sin alpha sin beta, cos alpha ) ]:} =0