If $$cosec^4θ=49+cot^4θ$$​, what is the value of sin $$θ$$​?

Correct option is B

Given:

​$$cosec^4θ=49+cot^4θ$$

Formula Used:

1 + $$cot^2\theta = coseec^2\theta$$

Solution:

​$$cosec^4θ=49+cot^4θ \\ \ \\cosec^4θ -cot^4θ=49 \\ \ \\(cosec^2θ -cot^2θ)(cosec^2θ +cot^2θ) =49 \\ \ \\1\times(cosec^2θ+cosec^2θ -1) =49 \\ \ \\2 cosec^2θ= 49 +1 \\ \ \\cosec^2θ = \frac {50}2 \\ \ \\cosec^2θ =25 \\ \ \\\frac {1}{sin^2θ}=25 \\ \ \\sin θ =\frac 15$$​​