Question

If \[\sin \theta = \frac{4}{5}\] what is the value of cotθ + cosecθ? 

Answer 1

Given: `sin θ=4/5` 

We know that, 

`sin^2 θ+cos^2=1` 

⇒ `(4/5)^2+cos^2 θ=1` 

⇒ `16/25+cos^2 θ=1` 

⇒ `cos^2θ=1-16/25` 

⇒`cos^2θ=9/25` 

⇒`cosθ=3/5` 

We have, 

`cos θ+cosec θ=cosθ/sin θ+1/sinθ` 

= `(3/5)/(4/5)+1/(4/5)` 

= `3/4+5/4` 

= `2`

Hence, the value of cotθ + cosecθ is 2.