Establish this identity:
tan(θ)cot(θ)-sin^2(θ) = cos^2(θ)

Question

Establish this identity: 
tan(θ)cot(θ)-sin^2(θ) = cos^2(θ)

jim_thompson5910 · Answer

hint: cot(x) = 1/tan(x) and sin^2(x) + cos^2(x) = 1

luigi0210 · Answer

Easy, what's tan and cot in terms of sin/cos?

anonymous · Answer

did you eat magic beans?

luigi0210 · Answer

Me and Jim have different methods, but same result

anonymous · Answer

Gah. I'll come back to this tomorrow, I've been doing homework for way to long. I'll look at it again tomorrow. Good night. Lol.

anonymous · Answer

it would be easier if you study "The Function Hexagon". It will make trigonometry simple. :)

tangent and cotangent are inverse functions right? so therefore it is equal to 1 when multiplied to each other.
now you have:

1-sin^2(theta) = cos^2(theta)

look back again the formula,

sin^2(theta)+cos^2(theta) = 1

if we transpose "sin^2(theta)" to the other side, it will be:

cos^2(theta) = 1-sin^2(theta)

right? now you proved it.

cos^2(theta) = cos^2(theta)

anonymous · Answer

Oh okay I see what you did.  and the tan was like adding fractions . . .  cot and the tan was like adding fractions . . . Brain fart. Thank you so much for your help. :)