If ` tantheta-cottheta=aandsintheta+costheta=b(b^2-1)^2(a^2+4)` is equal to

Options

A. 2
B. `-4`
C. `pm 4`
D. 4

Answer

D

Explanation

Given that `tan theta-cot theta = alpha`
and `sin theta + cos theta = b` …..(1)
Now `(b^(2)-1)^(2)(a^(2)+4)` ……(2)
`=[(sin theta + cos theta)^(2)(tan theta - cot theta)^(2)+4]`
`=[1+2sin theta.cos theta-1]^(2)(tan^(2)theta+cot^(2)theta-2+4]`
`=4sin^(2)cos^(2)theta[(1)/(sin^(2)theta)+(1)/(cos^(2)theta)]=4`