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

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Answer 1 · 2018-03-08T18:27:14

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$RHS: +-tan theta/(sqrt(1+tan^2theta))$

$=+-tan theta/sqrt(sec^2theta)$

$=tan theta/sec theta$ ->since we are squaring $sectheta$ the result is always positive so we drop the negative sign.

$=(sin theta/cos theta)/(1/costheta)$

$=sin theta/cancelcos theta * cancelcos theta/1$

$=sin theta$

$=LHS$

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