`sin (alpha + beta) - 2 sin alpha cos beta + sin (alpha - beta)` किसके बराबर है ?

What is sin (alpha+beta) - 2 sin alpha cos beta + sin(alpha- beta) =

sin alpha + sin beta = a, cos alpha + cos beta = b rArr sin (alpha + beta)

sin alpha + sin beta = a "and" cos alpha + cos beta = b sin (alpha + beta) =

sin ^ (2) alpha + sin ^ (2) (alpha-beta) -2sin alpha cos beta sin (alpha-beta) = sin ^ (2)

If sin alpha + sin beta = a , cos alpha + cos beta = b " then sin ( alpha + beta ) =

(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 + cos beta)/( sin alpha - sin beta) + (sin alpha + sin beta)/( cos alpha - cos beta ) =

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

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