Mathematics: Tantheta+sintheta/tantheta-sintheta=sectheta+1/sectheta-1

Tantheta+sintheta/tantheta-sintheta=sectheta+1/sectheta-1

tyreshagarrett123

15.06.2021

TO PROVE :-

$\frac{\tan \theta + \sin \theta}{\tan \theta - \sin \theta} = \frac{\sec \theta + 1}{\sec \theta - 1}$

SOLUTION :-

First of all , simplify L.H.S.

$\frac{\tan \theta + \sin \theta}{\tan \theta - \sin \theta}$

Use $\tan \theta = \frac{\sin \theta}{\cos \theta}$ in place of tanθ.

$= \frac{\frac{\sin \theta}{\cos \theta} + \sin \theta }{\frac{\sin \theta}{\cos \theta} - \sin \theta}$

Take sinθ common from both numerator & denominator.

$= \frac{\sin \theta (\frac{1}{\cos \theta} + 1) }{\sin \theta (\frac{1}{\cos \theta}- 1) }$

Cancel the sinθ from both numerator & denominator.

$= \frac{\frac{1}{\cos \theta} +1}{\frac{1}{\cos \theta} -1}$

Use $\sec \theta = \frac{1}{\cos \theta}$

$= \frac{\sec \theta + 1}{\sec \theta - 1}$

∴ L.H.S. = R.H.S

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foxrule

03.02.2021

She wants the construction to move more quickly

Step-by-step explanation:

this was the correct answer as shown on the quiz. the choices were changed

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