Let f(θ) = sinθ(sinθ + sin 3θ). Then, f(θ) — JEE Main 2000 Mathematics PYQ

2000

Let

f(\theta) = \sin\theta(\sin\theta + \sin 3\theta)

. Then,

f(\theta)

A.
$\geq 0$ only when $\theta \geq 0$
B.
$\leq 0$ for all real $\theta$
C.
$\geq 0$ for all real $\theta$
D.
$\leq 0$ only when $\theta \leq 0$

Show answer and solution

Correct option: C

Solution

f(θ) = sinθ(sinθ + sin3θ). Use the sum-to-product identity: sinθ + sin3θ = 2sin2θcosθ. So f(θ) = sinθ · 2sin2θcosθ = 2sinθcosθ · sin2θ = sin2θ · sin2θ = sin²(2θ). Since sin²(2θ) ≥ 0 for all real θ, f(θ) ≥ 0 always.

[2000]

Practise Trigonometry the way it is asked

A timed set of real JEE Main Trigonometry questions, graded as the exam grades. No sign-up.

Start a Trigonometry test

More: all JEE Main Trigonometry questions · JEE Main 2000 · Mathematics chapter list

JEE Main 2000 Mathematics question on Trigonometry