JEE Main 2019MathematicsTrigonometric Ratios & IdentitiesEasyMCQ

JEE Main 2019 — Trigonometric Ratios & Identities Question with Solution

JEE Main 2019 (09 Apr Shift 2)

Question

The value of sin10°sin30°sin50°sin70° is:

Choose an option

Show full solutionCorrect option: B
Correct answer
B116

Step-by-step explanation

sin10°sin30°sin50°sin70°

=sin10°×1212×2sin50°sin70°

=14sin10°2sin50°sin70°

Using 2sinAsinB=cosA-B-cosA+B

=14sin10°cos20°-cos120°

=14sin10°cos20°-cos90°+30°

=14sin10°cos20°+sin30°

=14sin10°cos20°+12

=182sin10°cos20°+sin10°

Again, using 2sinAcosB=sinA+B-sinA-B 

=18sin30°-sin10°+sin10°

=1812=116.

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About this question

This is a previous-year question from JEE Main 2019, covering the Trigonometric Ratios & Identities chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.