Mathematics: Jorge owes his father $60. after raking the lawn for the month, he has paid him $12, $8, and $9. how much money does jorge still has owes his father?

Jorge owes his father $60. after raking the lawn - id601161844, byrdkellykellybyrd

tyreshagarrett123

29.06.2022

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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