Question

If sin thita+cosec thita=3,find the value of sin^2thita+cosec^2thita.
​

Answer 1

Explanation:

sin^2thita+cosec^2thita. = 1,

it have nothing to do with the given values!

Answer 2

7

Explanation:

using the identities

• (sinΘ + cosecΘ)² = sin²Θ + 2sinΘcosecΘ + cosec²Θ

• cosecΘ =
`(1)/(sin0)`

then

2sinΘcosecΘ = sinΘ ×
`(1)/(sin0)` = 1

Hence

sin²Θ + 2sinΘcosecΘ + cosec²Θ = (sinΘ + cosecΘ)² = 3² = 9

sin²Θ + 2 + cosec²Θ = 9 ( subtract 2 from both sides )

sin²Θ + cosec²Θ = 7