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Maths Trigonometrical Ratios, Functions and Identities Mix Comprehension

Published by: CGP EDU Academic Team

Published on: August 14, 2026

Given sin x < x < tan x where x ∈ then answer the following

(i) If a = cos (sin x), b = sin (cos x) then –

Correct Answers for Comprehension Sub-Questions

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The correct answer is:

CHECK THE SOLUTION.

(i)

a – b = cos (sin x) – sin (cos x)

= sin – sin (cos x)

= 2 cos

sin

∴ sin x ± cos x ∈ [– , ]

So ∈

∴ ± ∈

So a – b > 0

(ii)

sin x < x

So cos x >

⇒ < ⇒ tan x <

(iii)

Sol. If log (sin x + cos x) < x

Then 2 log (sin x + cos x) < 2x

⇒ log (sin x + cos x) 2 < 2x

⇒ log (1 + sin 2x) < 2x

Which is true as log (1 + x) < x, ∀ x > 0

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