Question

Verify that the statement is an identity.

csc x(sec x - 2 cos x)
=
tan x
cot x

Answer 1

-2cot(2x)

Explanation:

= csc(sec x - 2 cos x)

= -csc(2cos x - sec x)

= -csc(2cos x - 1/cosx)

= -csc((2cos^2 x - 1)/cos x)

= -csc(cos 2x /cos x)

= (-1/sin x) (cos 2x /cos x)

= -cos 2x / sin x cos x

= -2cos 2x / 2sin x cos x

= -2cos 2x / sin 2x

= -2cot 2x