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How do you prove sintheta=+-tantheta/(sqrt(1+tan^2theta))?

Mar 8, 2018

See Below

Explanation:

$R H S : \pm \tan \frac{\theta}{\sqrt{1 + {\tan}^{2} \theta}}$

$= \pm \tan \frac{\theta}{\sqrt{{\sec}^{2} \theta}}$

$= \tan \frac{\theta}{\sec} \theta$->since we are squaring $\sec \theta$ the result is always positive so we drop the negative sign.

$= \frac{\sin \frac{\theta}{\cos} \theta}{\frac{1}{\cos} \theta}$

$= \sin \frac{\theta}{\cancel{\cos}} \theta \cdot \cancel{\cos} \frac{\theta}{1}$

$= \sin \theta$

$= L H S$