How do you evaluate ${tan}^{- 1} (sin (\frac{π}{2}))$ $tan^-1(sin(pi/2))$ without a calculator?

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Answer 1 · 2016-11-04T06:07:54

${tan}^{- 1} (sin (\frac{π}{2})) = \frac{π}{4}$ $tan^(-1)(sin(pi/2))=pi/4$

As $sin (\frac{π}{2}) = 1$ $sin(pi/2)=1$ and $tan (\frac{π}{4}) = 1$ $tan(pi/4)=1$

${tan}^{- 1} (sin (\frac{π}{2})) = {tan}^{- 1} 1 = \frac{π}{4}$ $tan^(-1)(sin(pi/2))=tan^(-1)1=pi/4$

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