Letf(θ)=sin⁡θ(sin⁡θ+sin⁡3θ).Thenf(θ)

Let $f (θ) = \sin θ (\sin θ + \sin 3 θ) .$ Then $f (θ)$

A
$⩾$ $0$ only when $θ ⩾ 0$
B
$⩽ 0$ for all $θ$
C
$⩾ 0$ for all $θ$
D
$⩽ 0$ only when $θ ⩽ 0$

Solution:

$f (θ)$ $= \sin θ$ $(\sin θ + \sin 3 θ)$

$= \sin θ . 2 \sin 2 θ \cos θ = 2 \sin θ \cos θ \sin 2 θ$

$= \sin^{2} 2 θ ⩾ 0$ for all $θ$

Related content

JEE Main 2023 Question Papers with Solutions

JEE Main 2024 Syllabus

Best Books for JEE Main 2024

JEE Advanced 2024: Exam date, Syllabus, Eligibility Criteria

JEE Main 2024: Exam dates, Syllabus, Eligibility Criteria

JEE 2024: Exam Date, Syllabus, Eligibility Criteria

NCERT Solutions For Class 6 Maths Data Handling Exercise 9.3

JEE Crash Course – JEE Crash Course 2023

NEET Crash Course – NEET Crash Course 2023

JEE Advanced Crash Course – JEE Advanced Crash Course 2023