Question

if tan theta = -5/12 then find the value of (2 cos theta )/(1- sin theta) ​

Answer 1

Answer:

Cosθ+Sinθ=717

Step-by-step explanation:

Tan \theta = \frac{Perpendicular}{Base}Tanθ=BasePerpendicular

We are given that Tan \theta = \frac{5}{12}Tanθ=125

On comparing ,

Perpendicular = 5

Base = 12

To find Hypotenuse we will use Pythagoras theorem

\begin{gathered}Hypotenuse^2 = Perpendicular^2+Base^2\\Hypotenuse^2 = 5^2+12^2\\Hypotenuse=\sqrt{5^2+12^2}\\Hypotenuse = 13\end{gathered}Hypotenuse2=Perpendicular2+Base2Hypotenuse2=52+122Hypotenuse=52+122Hypotenuse=13

Sin \theta = \frac{Perpendicular}{Hypotenuse}Sinθ=HypotenusePerpendicular

Sin \theta = \frac{5}{13}Sinθ=135

Cos\theta = \frac{Base}{Hypotenuse}Cosθ=HypotenuseBase

Cos\theta = \frac{12}{13}Cosθ=1312

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}Cosθ−SinθCosθ+Sinθ=1312−1351312+135=717

Hence \frac{Cos \theta +Sin \theta}{Cos \theta - Sin \theta} =\frac{17}{7}Cosθ−SinθCosθ+Sinθ=717

Step-by-step explanation:

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Answer 2

Answer:

Cosθ+Sinθ=717

Step-by-step explanation:

Tan \theta = \frac{Perpendicular}{Base}Tanθ=BasePerpendicular

We are given that Tan \theta = \frac{5}{12}Tanθ=125

On comparing ,

Perpendicular = 5

Base = 12

To find Hypotenuse we will use Pythagoras theorem

\begin{gathered}Hypotenuse^2 = Perpendicular^2+Base^2\\Hypotenuse^2 = 5^2+12^2\\Hypotenuse=\sqrt{5^2+12^2}\\Hypotenuse = 13\end{gathered}Hypotenuse2=Perpendicular2+Base2Hypotenuse2=52+122Hypotenuse=52+122Hypotenuse=13

Sin \theta = \frac{Perpendicular}{Hypotenuse}Sinθ=HypotenusePerpendicular

Sin \theta = \frac{5}{13}Sinθ=135

Cos\theta = \frac{Base}{Hypotenuse}Cosθ=HypotenuseBase

Cos\theta = \frac{12}{13}Cosθ=1312

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}Cosθ−SinθCosθ+Sinθ=1312−1351312+135=717

Hence \frac{Cos \theta +Sin \theta}{Cos \theta - Sin \theta} =\frac{17}{7}Cosθ−SinθCosθ+Sinθ=717

Step-by-step explanation:

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