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Question

If cos1(23x)+cos1(34x)=π2 (x>34), then x is equal to:

A
14512
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B
14612
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C
14511
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D
14510
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Solution

The correct option is A 14512
Given : cos1(23x)+cos1(34x)=π2
cos1(23x)=π2cos1(34x)
cos1(23x)=sin1(34x)[sin1y+cos1y=π2]
cos1(23x)=cos11(34x)2
Applying cos both sides, we get
23x=1(34x)2
49x2=1(34x)2
49x2+916x2=1
64+819×16×x2=1
x=14512 [x>34]

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