Question

If tan theta= 3/4 , find csc theta

Answer 1

`csc\theta=(5)/(3)`

Explanation:

Given:

`tan\theta =(3)/(4)`

`cot\theta =(4)/(3)` [∵
`cot\theta =(1)/(tan\theta)` ]

Squaring both sides.

`cot^2\theta =(4^2)/(3^2)=(16)/(9)`

`csc^2\theta -1=(16)/(9)` [∵
`cot^2\theta =csc^2\theta-1]` ]

Adding 1 to both sides.

`csc^2\theta -1+1=(16)/(9)+1`

`csc^2\theta =(16)/(9)+1`

`csc^2\theta=(16)/(9) +(9)/(9)` [Taking LCD=9 and adding fractions ]

`csc^2\theta=(16+9)/(9)`

`csc^2\theta=(25)/(9)`

Taking square root both sides.

`√(csc^2\theta)=\sqrt{(25)/(9)}`

∴
`csc\theta=(5)/(3)`