Question

If cosecA + sinA = 2 then the value of cosec^50A +sin^50A
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Answer 1

Step-by-step explanation:

$\csc( \alpha ) + \sin( \alpha ) = 2 \\ \frac{1}{ \sin( \alpha ) } + \sin( \alpha ) = 2 \\ \frac{1 + \sin {}^{2} ( \alpha ) }{ \sin( \alpha ) } = 2 \\ 1 + \sin {}^{2} ( \alpha ) = 2 \sin( \alpha ) \\ 1 - 2 \sin( \alpha ) + \sin {}^{2} ( \alpha ) = 0 \\ (1 - \sin( \alpha ) ) {}^{2} = 0 \\ 1 - \sin( \alpha ) = 0 \\ \sin( \alpha ) = 1 \\ \alpha = 90 \\ \csc {}^{50} ( \alpha ) + \sin {}^{50} ( \alpha ) \\ \csc {}^{50} (90) + \sin {}^{50} (90) \\ 1 + 1 = 2$