`(sinalpha cos beta+cos alpha sin beta)^2+(cos alpha cos beta-sin alpha sin beta)^2=1`

Prove that (sin alpha cos beta + cos alpha sin beta) ^(2) + (cos alpha coa beta - sin alpha sin beta) ^(2) =1.

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|

(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

det[[cos alpha cos beta,cos alpha sin beta,-sin alpha-sin beta,cos beta,0sin alpha cos beta,sin alpha sin beta,cos alpha]]

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 ,,,|cos alpha cos beta,cos alpha sin beta,-sin alpha-sin beta,cos beta,0sin alpha,cos beta,sin alpha sin beta,cos alpha]|

A = [[0, sin alpha, sin alpha sin beta-sin alpha, 0, cos alpha cos beta-sin alpha sin beta, -cos alpha cos beta, 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 ) |:} =1

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