JEE Main 2019MathematicsMatricesMediumMCQ

JEE Main 2019 — Matrices Question with Solution

JEE Main 2019 (09 Jan Shift 1)

Question

If A=cosθ-sinθsinθcosθ , then the matrix A-50 when θ=π12, is equal to:

Choose an option

Show full solutionCorrect option: A
Correct answer
A3212-1232

Step-by-step explanation

A=cosθ-sinθsinθcosθ⇒A=cosθ-sinθsinθcosθ=cos2θ+sin2θ=1

And adjA=cosθsinθ-sinθcosθ

⇒A-1=1AadjA=cosθsinθ-sinθcosθ

⇒A-2=A-12=A-1A-1

=cosθsinθ-sinθcosθcosθsinθ-sinθcosθ

=cos2θ-sin2θ2sinθcosθ-2sinθcosθcos2θ-sin2θ

=cos2θsin2θ-sin2θcos2θ

It is visible that

A-1n=cosnθsinnθ-sinnθcosnθ

⇒A-50=A-150=cos50θsin50θ-sin50θcos50θ

Now at θ=π12,sin50θ=sin50π12=sinπ6=12

cos50θ=cosπ6=32

⇒A-50=3212-1232

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About this question

This is a previous-year question from JEE Main 2019, 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.