Question

If $sin\Theta=\frac{4}{5}$, what is the value of cotθ + cosecθ?

Answer 1

Answer:

The value of cot θ + cosecθ is 2.

Step-by-step explanation:

Given : sin θ = ⅘ …….(1)

By using an identity , sin² θ + cos² θ = 1

(⅘)² + cos² θ = 1

16/25 + cos² θ = 1

cos² θ = 1 - 16/25

cos² θ = (25 - 16)/25

cos² θ = 9/25

cosθ = √9/25

cosθ = ⅗ …….(2)

cot θ + cosecθ  (Given)

cosθ/sin θ + 1/sinθ

[By using the identity, cotθ = cosθ/sinθ & cosecθ = 1/sinθ]

= (⅗)/(4/5) + 1/(⅘)

[From eq 1 & 2]

= ⅗ × 5/4 + 1 × 5/4

= ¾ + 5/4

= (3 + 5)/4

= 8/4

cot θ + cosecθ = 2  

Hence, the value of cot θ + cosecθ is 2.

HOPE THIS ANSWER WILL HELP YOU…

Answer 2

Solution :

Given, sinθ = 4/5

= perpendicular / hypotenuse

∴ perpendicular = 4 units

& hypotenuse = 5 units

∴ base = √(5² - 4²) units

= 3 units

Then, cotθ = base / perpendicular

= 3/4

and cosecθ = 1/sinθ

= 1/(4/5)

= 5/4

∴ cotθ + cosecθ

= 3/4 + 5/4

= (3 + 5)/4

= 8/4

= 2 (Ans.)