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Question

If for some θ lying between 0° and 90°, tanθ = 1, then what is the value of sin 2θ - 2sinθ cosθ ?

This question was previously asked in
CDS II 2021 General Knowledge Previous Year Paper (14-Nov-2021)
The correct answer is

-1/2

Given:

tanθ = 1; 0º < θ < 90º

Formula used:

tan 45º = 1

sin 45º = 1/√2

cos 45º = 1/√2

Calculation:

We have, tanθ = 1

⇒ tanθ = tan45° 

⇒ θ = 45º

Now, we need to find the value of sin2θ - 2sinθ cosθ when θ = 45º

⇒ sin245º - 2 sin45º cos45º

⇒ (1/2) - 2(1/√2)(1/√2)

∴ sin2θ - 2sinθ cosθ = - 1/2

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  2. What is (1 + cot θ - cosec θ)(1 + tan θ + sec θ) equal to?

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Important Questions from Trigonometric Ratios and Identities

  1. What is the ratio of the greatest to the smallest value of 2 – 2 sin x – sin 2x, 0 ≤ x ≤ (π/2)? 

  2. If sinθ = \(\frac{4}{5}\) , Find the value of sin3θ

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