Question

prove that sin a minus sin beta upon cos theta minus Cos a = COt (a + beta) upon 2​

Answer 1

Given that,

[sinαsinβ−cosαcosβ+1=0]

Then,

⇒sinαsinβ−cosαcosβ=−1

⇒−(cosαcosβ−sinαsinβ)=−1

⇒cosαcosβ−sinαsinβ=1

⇒cos(α+β)=1

⇒cos(α+β)=cos0

0

Then,

(α+β)=0

α=−β...................(1)

L.H.S.

1+cotαtanβ

By equation (1)

1+cot(−β)tanβ

=1−cotβtanβ Since, cot(−θ)=cotθ

=1−cotβ.

cotβ

1

=1−1

=0

L.H.S.=R.H.S.

Hence proved