Question

If sin θ + cos θ = a and sec θ + cosec θ = b , then the value of b (a2 – 1) is equal to *​

Answer 1

Given, secθ+cscθ=b and sinθ+cosθ=a  

sinθ1 +cos1 =b

⇒sinθcosθsinθ+cosθ  =b

sinθcosθa​  

=b ⇒sinθcosθ=ba

Now consider, sinθ+cosθ=a

Squaring on both the sides we get,  

(sinθ+cosθ)2 =a2 ⇒sin 2 θ+cos2θ+2sinθcosθ=a 2 ⇒1+ b2a =a2

⇒ b(b+2a) =a2

⇒(b+2a)=a 2 b

⇒2a=a 2 b−b

⇒2a=b(a2 −1)

Hence, the answer is 2a.

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Answer 2

Step-by-step explanation:

solution is in the picture