JEE Main 2021MathematicsProperties of TrianglesHardMCQ

JEE Main 2021 — Properties of Triangles Question with Solution

JEE Main 2021 (27 Aug Shift 1)

Question

Let sinAsinB=sin(A-C)sin(C-B), where A, B, C are angles of a triangle ABC. If the lengths of the sides opposite these angles are a, b, c respectively, then

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Correct answer
Ab2,c2,a2 are in A.P.

Step-by-step explanation

Let sin Aa=sin Bb=sin Cc=k⇒sin A=ak, sin B =bk & sin C=ck

As A+B+C=π

⇒B+C=π-A , ⇒sinB+C=sinπ-A=sin A

Similarly, sinA+C=sin B

⇒sinB+CsinA+C=sinA-CsinC-B

⇒sinB+CsinC-B=sinA+CsinA-C

⇒sin2C-sin2B=sin2A-sin2C

⇒c2-b2=a2-c2 ⇒2c2=a2+b2

therefore we can say that b2,c2,a2 are in A.P.

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About this question

This is a previous-year question from JEE Main 2021, covering the Properties of Triangles 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.