Scratch paper if needed should be organized and stapled to t

Scratch paper (if needed) should be organized and stapled to the back of this sheet. Show credit may be given. Answers must be exact (unless otherwise stated), simplified and clear the blanks provided. 1-cos-1-cosx = 4cotxesex 1-cosx = 4 cot x csex 1 cos x 1 cos x 1+cos x 1. Verify the identity 1-cosx cos x

Solution

(1+cosx)/(1-cosx) - (1-cosx)/(1+cosx) = 4cotxcscx

LHS : taking (1-cosx)(1+cosx) as LCD:

= [(1+cosx)^2 - (1-cosx)^2 ]/(1-cos^2x)

={ 1 +cos^2x +2cosx - 1 - cos^2x +2cosx}/sin^2x

= 4cosx/sin^2x

=4(cosx/sinx)(1/sinx)

=4cotx*cscx

RHS