given cot teta=7/8 then evaluate( 1+sin teta/cos teta)
Answers
Answer:
2.6614
Step-by-step explanation:
We know that Cot \theta = \frac{Base}{Perpendicular}Cotθ=
Perpendicular
Base
We are given that cot \theta= \frac{7}{8}cotθ=
8
7
On comparing
Base = 7
Perpendicular = 8
To find hypotenuse we will use Pythagoras theorem
Hypotenuse^2 = Perpendicular^2+Base^2Hypotenuse
2
=Perpendicular
2
+Base
2
Hypotenuse^2 = 8^2+7^2Hypotenuse
2
=8
2
+7
2
Hypotenuse^2 = 64+49Hypotenuse
2
=64+49
Hypotenuse^2 = 113Hypotenuse
2
=113
Hypotenuse = \sqrt{113}Hypotenuse=
113
Sin\theta = \frac{Perpendicular}{Hypotenuse}Sinθ=
Hypotenuse
Perpendicular
Sin\theta = \frac{8}{\sqrt{113}}Sinθ=
113
8
Cos\theta = \frac{Base}{Hypotenuse}Cosθ=
Hypotenuse
Base
Cos\theta = \frac{7}{\sqrt{113}}Cosθ=
113
7
Now we are supposed to find \frac{1+sin\theta}{cos \theta}
cosθ
1+sinθ
Substitute the values
=\frac{1+\frac{8}{\sqrt{113}}}{\frac{7}{\sqrt{113}}}=
113
7
1+
113
8
=2.6614=2.6614
Hence \frac{1+sin\theta}{cos \theta}=2.6614
cosθ
1+sinθ
=2.6614
Step-by-step explanation:
I hope this will help you