JEE Main 2021MathematicsTrigonometric Ratios & IdentitiesEasyMCQ

JEE Main 2021 — Trigonometric Ratios & Identities Question with Solution

JEE Main 2021 (18 Mar Shift 2)

Question

If 15sin4α+10cos4α=6, for some α∈R, then the value of 27sec6α+8cosec6α is equal to :

Choose an option

Show full solutionCorrect option: D
Correct answer
D250

Step-by-step explanation

15sin4α+10cos4α=6

15sin4α+10cos4α=6sin2α+cos2α2

3sin2α-2cos2α2=0

∴ 3sin2α-2cos2α=0

tan2α=23 & cot2α=32

⇒27sec6α+8cosec6α

=27sec2α3+8cosec2α3

=271+tan2α3+81+cot2α3

=271+233+81+323

=250

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Trigonometric Ratios & Identities chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.

Solve interactively →

About this question

This is a previous-year question from JEE Main 2021, 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.