Question

Please answer this question​

Answer 1

*answer in the attachment.

Answer 2

Given--->

2 Sinα Cosβ Sinγ = Sinβ Sin ( α + γ )

To prove ---> tanα , tanβ , tanγ are in HP

Solution--->

1) plzz refer the attachment

2) We know that to prove tanα , tanβ , tanγ are in HP it is sufficient to prove that

1 / tanα , 1 / tanβ , 1 / tanγ are in AP i. e.

Cotα , Cotβ , Cotγ are in AP .

3) For this we proceed with given expression and applying a formula in 2nd step as follows

Sin ( α + γ ) = Sinα Cosγ + Cosα Sinγ

4) In fourth step we divide whole equation by sinα Sinβ Sinγ

5) We know that ,

Cotθ = Cosθ / Sinθ , and applying it in 6th step

6) We know that if

a + c = 2b , then a , b , c are in AP

Applying it in 7th step

7) We know that

tanθ = 1 / Cotθ ,applying it second last step

8) We know that if

1 / a , 1 / b , 1 / c are in AP , then

a , b , c are in HP .