Question

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

Answer 1

Answer:

$\huge \theta =7°$

Step-by-step explanation:

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