cos x 12 cos x 12cos2 x 1 Solutioncosx 12 cosx 12cos2x 1

(cos x - 1)^2 - (cos x + 1)^2/cos^2 x - 1

Solution

[(cosx -1)² -(cosx +1)²]/[cos²x -1]

(a-b)²=a²-2ab+b²,(a+b)²=a²+2ab+b²,

[(cos²x -2cosx +1) -(cos²x +2cosx +1)]/[cos²x -1]

[cos²x -2cosx +1 -cos²x -2cosx -1]/[cos²x -1]

[ -2cosx -2cosx ]/[cos²x -1]

[ -4cosx ]/[cos²x -1]

we have identity sin²x +cos²x=1 ,so cos²x-1=-sin²x

[ -4cosx ]/[-sin²x]

[ 4cosx ]/[sin²x]

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

=4 cotx cscx