Question

Given cot teta=7/8, then evaluate
(1+sin teta)/cos teta.​

Answer 1

We know that Cot \theta = \frac{Base}{Perpendicular}
We are given that cot \theta= \frac{7}{8}
On comparing
Base = 7
Perpendicular = 8
To find hypotenuse we will use Pythagoras theorem
Hypotenuse^2 = Perpendicular^2+Base^2
Hypotenuse^2 = 8^2+7^2
Hypotenuse^2 = 64+49
Hypotenuse^2 = 113
Hypotenuse = \sqrt{113}
Sin\theta = \frac{Perpendicular}{Hypotenuse}
Sin\theta = \frac{8}{\sqrt{113}}
Cos\theta = \frac{Base}{Hypotenuse}
Cos\theta = \frac{7}{\sqrt{113}}
Now we are supposed to find \frac{1+sin\theta}{cos \theta}
Substitute the values
=\frac{1+\frac{8}{\sqrt{113}}}{\frac{7}{\sqrt{113}}}
=2.6614
Hence \frac{1+sin\theta}{cos \theta}=2.6614