Question

(sin x)(tan x cos x - cot x cos x) = 1 - 2 cos2x

Verify each trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side of the equation.

Answer 1

I would begin with the left side:
Maybe it is a good idea to get rid of tan x and cot x:\[\sin x \left( \frac{ \sin x }{ \cos x }\cos x - \frac{ \cos x }{ \sin x }\cos x \right)=\]

Answer 2

howd you get the formulas

Answer 3

Mmm... one is supposed to know that\[\tan x=\frac{ \sin x }{ \cos x }\]and
\[\cot x=\frac{ cos x }{ \sin x }\]

BTW shouldn't the right hand side be 1-2cos²x?

Answer 4

that is correct, and thank you.

Answer 5

So, left hand side is now only:\[\sin^2x-\cos^2x\]What to do next?

Answer 6

convert sin to cos?

Answer 7

That will work.
You'll have to know yet another formula then ;)

Answer 8

sin^(2)x+cos^(2)x=1?

Answer 9

Yes, rewrite to get sin²x...

Answer 10

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

Answer 11

No, if\[\sin^2x+\cos^2x=1\]then\[\sin^2x=1-\cos^2x\]Now you have:on the left hand side:
\[1-\cos^2x-\cos^2x\]Compare this with the right hand side...