Question

if tan theta=3/4,find the value of cosec theta

Answer 1

Hi mate!

Answer:

5/3

Step-by-step explanation:

In this question we are going to use the identity:-

cosec²θ = 1 + cot²θ  or  cosec²θ - cot²θ = 1   ( both are same if u simplify it)

so we have to find cosecθ

so in the formula it is square(²) of cosec but we want only cosecθ so we will square root on both sides

then we will have,

cosecθ=√(1+cot²θ)    (now we have the perfect formula)

now only we need is cot²θ but basically only cotθ then we will square it and then we get cot²θ

so we are given the value of tanθ that is:- tanθ=3/4

also, we know that tanθ=1/cotθ, right?

so cotθ = 1/tanθ  (just exchanged the places like cross multiply)

so cotθ= 1/(3/4)    (as tanθ=3/4 so I replaced it in the equation)

so cot θ = 4/3     (just simplified it)

now we have cotθ=4/3 but we need cot²θ so we square both the sides

cot²θ=(4)²/(3)²=16/9

now we will replace the value of cot²θ in our formula :- cosecθ=√(1+cot²θ)

so cosecθ=√(1+(16/9))

                =√((9+16)/9)

                =√(25/9)

                = (√25)/(√9)

so we have  cosec θ = (√25)/(√9)

We know √25=5  and √9=3

so cosecθ = √25)/(√9) = 5/3

final answer -------  COSECθ = 5/3

Hope you understood my solution!

Thank you and if possible then plz mark my answer as the BRAINLIEST (ur wish but it would really help me :)

bye!!