Write the expression in terms of sine and cosine and then si

Write the expression in terms of sine and cosine, and then simplify so that no quotients appear in the final expression.

-sin^2 theta( csc ^2 theta-1)

choose the correct answer below

a) csc ^2

b)1/sin^2 theta

c)-cos ^2 theta

d) tan ^2 theta

e) -1/ sin^2 theta

f) cos ^2 theta

Solution

-sin^2 theta( csc ^2 theta-1)

= -sin^2theta*csc^2theta + sin^2theta

we know sintheta = 1/csctheta

So, sin^2theta*csc^2theta = 1

= -1 +sin^2theta

Now , we know sin^2theta +cos^2theta =1

So, -1 +sin^2theta = - cos^2theta

Option C