JEE Main 2020MathematicsMatricesMediumMCQ

JEE Main 2020 — Matrices Question with Solution

JEE Main 2020 (06 Sep Shift 2)

Question

Let θ=π5 and A=cosθsinθ-sinθcosθ. If B=A+A4, then det B :

Choose an option

Show full solutionCorrect option: D
Correct answer
Dlies in 1, 2

Step-by-step explanation

A2=cosθsinθ-sinθcosθcosθsinθ-sinθcosθ

A2=cos2θsin2θ-sin2θcos2θ

⇒A4=cos4θsin4θ-sin4θcos4θ

B=cos4θsin4θ-sin4θcos4θ+cosθsinθ-sinθcosθ

=cos4θ+cosθsin4θ+sinθ-sin4θ+sinθcos4θ+cosθ

B=cos4θ+cosθ2+sin4θ+sinθ2

=2+2cos4θ·cosθ+sin4θ·sinθ

=2+2cos4θ-θ

=2+2cos3θ

B=2+2cos3π5

=2-5-12=5-52∈1,2

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About this question

This is a previous-year question from JEE Main 2020, covering the Matrices 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.