The value of ((Cos9ᵒ + Sin81ᵒ)(Sec9ᵒ + Cosec81ᵒ))/(2Sin²63ᵒ + 1 + 2Sin²27ᵒ) is:

The value of ((Cos9ᵒ + Sin81ᵒ)(Sec9ᵒ +…

The value of ((Cos9^o + Sin81^o)(Sec9^o + Cosec81^o))/(2Sin²63^o + 1 + 2Sin²27^o) is:

Show answer & explanation

Correct answer: A

Explanation

The correct answer is Option 1 i.e 4/3.

Understanding/Application

((Cos9⁰ + Sin81⁰)(Sec9⁰ + Cosec81⁰))/(2Sin²63⁰ + 1 + 2Sin²27⁰)

= {(cos(90 - 81) + sin81⁰)(sec(90 - 81) + cosec81⁰)}/{(2sin²63⁰ + 1 + 2sin²(90 - 63)}

= {(sin81⁰+ sin81⁰)(cosec81⁰ + cosec81⁰)}/(2sin²63⁰ + 1 + 2cos²63⁰)

= {(2sin81⁰) (2cosec81⁰)}/(3)

= 4/3