Question

if tan theta =5/12,find value of cos theta+sin theta /cos theta -sin theta.......​

Answer 1

Given :- tan$\theta$ = $\frac{5}{12}$

tan$\theta$=$\frac{p}{b}$=$\frac{5}{12}$

$h^2$=$\sqrt{5^2}+{12^2}$

$\sqrt{25}+{144}$

h = 13.

Now , we have to find value of :---

cos$\theta$+sin$\theta$

_______________

cos$\theta$ - sin$\theta$

$\frac{12}{13}$+$\frac{5}{13}$

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$\frac{12}{13}$ - $\frac{5}{13}$

$\frac{12+5}{13}$

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$\frac{12-5}{13}$

= $\frac{17}{13}$

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$\frac{7}{13}$

=$\frac{17}{13}$ X $\frac{13}{7}$

$\frac{17}{7}$ Ans.

Answer 2

$\frac{Cos \theta +Sin \theta}{Cos \theta - Sin \theta} =\frac{17}{7}$

Step-by-step explanation:

$Tan \theta = \frac{Perpendicular}{Base}$

We are given that $Tan \theta = \frac{5}{12}$

On comparing ,

Perpendicular = 5

Base = 12

To find Hypotenuse we will use Pythagoras theorem

$Hypotenuse^2 = Perpendicular^2+Base^2\\Hypotenuse^2 = 5^2+12^2\\Hypotenuse=\sqrt{5^2+12^2}\\Hypotenuse = 13$

$Sin \theta = \frac{Perpendicular}{Hypotenuse}$

$Sin \theta = \frac{5}{13}$

$Cos\theta = \frac{Base}{Hypotenuse}$

$Cos\theta = \frac{12}{13}$

So, $\frac{Cos \theta +Sin \theta}{Cos \theta - Sin \theta} = \frac{\frac{12}{13}+\frac{5}{13}}{\frac{12}{13}-\frac{5}{13}}=\frac{17}{7}$

Hence $\frac{Cos \theta +Sin \theta}{Cos \theta - Sin \theta} =\frac{17}{7}$

#Learn more :

If 5 tan theta is equal to 12 find the value of cos theta and sin theta

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