Question

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Ques:- If tan A=nTan B and sin A=m sin B, prove that cos^2 A=m^2-1/n^2-1



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Answer 1

i.e sinA/cosA=m.sinB/cosB

i.e sinA/sinB=m.cosA/cosB

i.e n.cosB=m.cosA ……..[from (1)]

Squaring both sides gives:

n2.cos2B=m2.cos2A

i.e n2.(1−sin2B)=m2.cos2A

i.e n2.(1−(sin2A/n2))=m2.cos2A …….[squaring (1)]

i.e n2−sin2A=m2.cos2A

i.e n2−1+cos2A=m2.cos2A [since sin^2A = 1 - cos^2A]

i.e n2−1=m2.cos2A−cos2A

i.e n2−1=cos2A(m2−1)

Hence, cos2A=(n2−1)/(m2−1)

Answer 2

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