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Question

The number of solutions of equation 5secθ13=12tanθ in [0,2π] is

A
2
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B
1
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C
4
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D
0
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Solution

The correct option is A 2
5secθ13=12tanθ
12sinθ+13cosθ=5
12313sinθ+13313cosθ=5313
Let cosα=13313sinα=12313
cosθ.cosα+sinθ.sinα=5313
cos(θα)=5313
Hence solution in the given interval is,
θ=αcos1(5313),α+cos1(5313)
Hence, option 'A' is correct.

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