How do we simplify $\frac{sin θ}{sin (θ + \frac{π}{2})}$ $sintheta/sin(theta + pi/2)$ ?

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How do we simplify $\frac{sin θ}{sin (θ + \frac{π}{2})}$ $sintheta/sin(theta + pi/2)$ ?

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Answer 1 · 2017-03-04T15:52:25

The expression equals $tan θ$ $tantheta$ .

Explanation:

We can expand the denominator using $sin (A + B) = sin A cos B + sin B cos A$ $sin(A + B) = sinAcosB + sinBcosA$ .

$\frac{sin θ}{sin θ cos (\frac{π}{2}) + sin (\frac{π}{2}) cos θ}$ $sintheta/(sinthetacos(pi/2) + sin(pi/2)costheta)$

$\frac{sin θ}{(0) sin θ + 1 (cos θ)}$ $sintheta/((0)sin theta + 1(costheta)$

$\frac{sin θ}{cos θ}$ $sintheta/costheta$

Use $tan θ = \frac{sin θ}{cos θ}$ $tantheta = sintheta/costheta$ :

$tan θ$ $tantheta$

Hopefully this helps!

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How do we simplify $\frac{sin θ}{sin (θ + \frac{π}{2})}$ $sintheta/sin(theta + pi/2)$ ?

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How do we simplify $\frac{sin θ}{sin (θ + \frac{π}{2})}$ $sintheta/sin(theta + pi/2)$ ?