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If tanA=ntanB, sinA=msinB then prove that …

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If tanA=ntanB, sinA=msinB then prove that cos2A=m2 - 1/n2-1

Posted by Mudit Kulshrestha 8 years ago

CBSE > Class 10 > Mathematics

1 answers

Rajeev Malhotra 8 years ago

SinA = m Sin B , Sin A/ Sin B = m and tan A= n tan B, tan A/tan B= n or Sin A/ cos A/Sin B/cos B= n , SinA Cos B / Cos A. Sin B= n

m² -1/ n² -1 = (Sin A / Sin B )² -1/(Sin ACos B /Cos A Sin B)² -1

= Sin²A/ Sin²B -1/ Sin²ACos²B/Cos²ASin²B -1

= Sin²A-Sin²B/ Sin²B/Sin²ACos²B - Cos²A Sin²B/ Cos²A Sin²B

= Sin²A - Sin²B x Cos²A Sin²B/Sin²B (Sin²A Cos²B - Cos²A Sin²B)

= Sin²A - Sin²B x Cos²A/ Sin²A(1- sin²B) - (1-Sin²A) Sin²B

= (Sin²A - Sin ²B ) x Cos²A /Sin²A - Sin²A Sin²B - Sin²B +Sin²A Sin²B

= (Sin²A - Sin²B) x Cos²A/ ( Sin²A - Sin²B)

= Cos ²A

1Thank You

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