Question

The expression
`(tan(x-(pi)/(2)).cos((3pi)/(2)+x)-sin^(3)((7pi)/(2)-x))/(cos(x-(pi)/(2)).tan((3pi)/(2)+x))`simplifies to
A. `(1+cos^(2)x)`
B. `sin^(2)x`
C. `-(1+cos^(2)x)`
D. `cos^(2)x`

Answer 1

Correct Answer - B
`(tan.(x-(pi)/(2)).cos.((3pi)/(2)+x)-sin^(3)((7pi)/(2)-x))/(cos(x-(pi)/(2)).tan((3pi)/(2)+x))`
`=((-cot)(sin x)+cos^(3)x)/((sin x).(-ct x))`
`=(-cos x + cos^(3)x)/(-cos x)`
`=1-cos^(2)x`
`=sin^(2)x`