Question

If Cos2a-sin2a=tan2b,prove that √2cosa.cosb=1

Answer 1

Solution :

It is given that ,

Cos²A - sin²A = tan²B

=>cos²A-(1-cos²A)= tan²B

[ Since , sin²A = 1 - cos²A ]

=>cos²A-1+cos²A= tan²B

=> 2cos²A-1 = tan²B

=> 2cos²A = tan²B + 1

=> 2cos²A = sec²B

[ Since , tan²B + 1 = sec² B ]

=> 2cos²A = 1/cos²B

=> 2cos²Acos²B = 1

Therefore ,

√(2cos²Acos²B) = √1

=> √2 cosAcosB = 1

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Answer 2

Hope this will help you