Question

Prove this identity: sin (-θ) cot (-θ)=cosθ

Answer 1

do you know what \(\cot(\theta)\) is?

Answer 2

yes, its cos θ=cosθ/sinθ

Answer 3

yes, except I think you meant "cot" and not "cos" on the left-hand-side there

Answer 4

yes I did haha, my bad

Answer 5

I'm confused on how i set it up?

Answer 6

so now you get:\[\sin(-\theta)\times\cot(-\theta)=\sin(-\theta)\times\frac{\cos(-\theta)}{\sin(-\theta)}\]

Answer 7

can you see what to do next?

Answer 8

not really, like do I cancel out the sinθ on the right side?

Answer 9

yes - so what will you be left with?

Answer 10

sin (-θ) X cot(-θ)=cos (-θ)

Answer 11

correct! almost there now....

Answer 12

do you know in which quadrants "cos" is positive?

Answer 13

no i don't

Answer 14

np, the "cos" function is positive in the first and 4th quadrants. which means:\[\cos(-\theta)=\cos(\theta)\]