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

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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..

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  1. 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)

    ML Aggarwal Solutions for Class 10 Chapter 18 - 50

    Hence, cot θ = √2 + 1

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