Question

How to find the θ in this equation: tan(θ+16°)=1/tan(θ+60°) by using the trigonometric identities?thanks

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Answer 1

`\huge \theta =7°`

Explanation:

`tan( \theta + 16 \degree) = (1)/(tan( \theta + 60 \degree) ) \\ tan( \theta + 16 \degree) =cot( \theta + 60 \degree) \\ tan( \theta + 16 \degree) = tan \{90 \degree - (\theta + 60\degree) \} \\ \theta + 16 \degree = 90 \degree - \theta - 60\degree \\ \theta +\theta = 30 \degree - 16\degree \\2 \theta = 14 \degree \\ \theta = (14 \degree)/(2) \\ \huge \red{ \boxed{\theta =7 \degree}}`