Question

4. If tan A = cot B, prove that A + B = 90°

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Answer 1

Step-by-step explanation:

$\tan( \alpha ) = \frac{1}{ \tan( \beta ) } \\ \\ \tan( \alpha ) \tan( \beta ) = 1 \\ \tan( \alpha + \beta ) = \frac{ \tan( \alpha ) + \tan( \beta ) }{1 - \tan( \alpha ) \tan( \beta ) } = \infty \\ \alpha + \beta = \frac{\pi}{2}$

Answer 2

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