This is an important question from the

Book- ML Aggarwal

Board- ICSE

Publication- Avichal

Chapter- Trigonometric Identities

Chapter number-18

If sin θ + cos θ = √2 sin (90° – θ), show that cot θ = √2 + 1

Trigonometric Identities, class 10th, chapter 18th, question no31 , ICSE board, ML aggarwal..

Given, sin θ + cos θ = √2 sin (90° – θ)

sin θ + cos θ = √2 cos θ

On dividing by sin θ, we have

1 + cot θ = √2 cot θ

1 = √2 cot θ – cot θ

(√2 – 1) cot θ = 1

cot θ = 1/ (√2 – 1)

Hence, cot θ = √2 + 1