Question

Verify the trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side of the equation.
(sin x)(tan x cos x - cot x cos x) = 1 - 2 cos^2 x

Answer 1

tan = sin/cos
So tan*cos = (sin/cos)*cos = sin

Answer 2

Then distribute in sin x.

Answer 3

so
(sin x)(tan x cos x - cot x cos x)
(sin x)(sin x - cot x cos x)

how would I simplify the cot x cos x part?

Answer 4

\[\sin(x)\left(\sin(x) - \frac{\cos(x)}{\sin(x)}\cos(x)\right)\]Multiply sin(x) by sinxover sinx:
\[\sin(x)\left(\frac{\sin^2(x)}{\sin(x)} - \frac{\cos(x)}{\sin(x)}\cos(x)\right)\]Combine fractions to get:\[\sin(x)\left(\frac{\sin^2(x) - \cos^2x}{\sin(x)} \right)\]

Cancel sin x

Answer 5

how does that equal 1 - 2 cos^2 x ?

Answer 6

thank you for your help btw

Answer 7

Did you cancel sin(x) yet?

Answer 8

I don't think I'm doing it correctly.

Answer 9

\[\cancel{\sin(x)}\left(\frac{\sin^2(x) - \cos^2x}{\cancel{\sin(x)}} \right)\]

Answer 10

lol oh i feel stupid. i was trying to cancel out sin^2 x on the numerator.

Answer 11

I'm still not sure how to get from sin^2 x - cos^2 x to 1-2cos^2 x

Answer 12

Hint:
\(\sin^2x = 1 - \cos^2x\) (by Pythagorean Identity)

Answer 13

oooh
1 - cos^2 x - cos^2 x = 1- 2 cos^2 x
thank you so much