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