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प्रश्न
Solve for x:
`2tan^(-1)(cosx)=tan^(-1)(2"cosec" x)`
उत्तर
`2tan^(-1)(cosx)=tan^(-1)(2"cosec" x)`
`=>tan^(-1)((2cosx)/(1-cos^2x))=tan^(-1)(2"cosec" x) ""[because 2tan^(-1)x=tan^(-1)(2x/(1-x^2))]`
`=>(2cosx)/(sin^2x) = 2"cosec" x`
`=>(cosx)/(sin^2x) = 1/sinx`
`=>(sinx)/(cosx) = 1`
`=>tanx = 1`
`=> x=pi/4`
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