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Question

If cos xa=sin xb then |a cos 2x+b sin 2x|=


A

|a|

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B

|aab|

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C

a2|b|

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D

b2|a|

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Solution

The correct option is A

|a|


cosxa=sinxb
tanx=ba
sin 2x=2tanx1+tan2x=2aba2+b2cos2x=1tan2x1+tan2x
cos2x=1b2a21+b2a2
cos2x=a2b2a2+b2acos2x+bsin2x=a(a2b2)a2+b2+b(2ab)a2+b2=a3ab2+2ab2a2+b2=a3+ab2a2+b2=(a2+b2)a2+b2=a


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