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6 votes
6 votes
Verify that the statement is an identity.

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

User Shivam Bhalla
by
2.7k points

1 Answer

22 votes
22 votes

Answer:

-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

User Rambles
by
2.6k points