Question

Verify the Identity:
cot(x-pi/2)=-tanx

Need help solving, will medal immediately. (:

Answer 1

hint: \(\bf cot\left( x-\frac{\pi }{2} \right)\implies \cfrac{cos\left( x-\frac{\pi }{2} \right)}{sin\left( x-\frac{\pi }{2} \right)}
\\ \quad \\
\cfrac{cos(x)cos\left(\frac{\pi }{2} \right)+sin(x)sin\left(\frac{\pi }{2} \right)}{sin(x)cos\left(\frac{\pi }{2} \right)-cos(x)sin\left(\frac{\pi }{2} \right)}\)

Answer 2

@jdoe0001 I'm still confused as to how to verify the identity

Answer 3

well... what's the \(cos\left(\frac{\pi }{2} \right)?\)
what about the \(sin\left(\frac{\pi }{2} \right) ?\)

Answer 4

The cos is 0 and the sin is 1, correct? @jdoe0001

Answer 5

yes so... .one sec

Answer 6

\(\bf cot\left( x-\frac{\pi }{2} \right)\implies \cfrac{cos\left( x-\frac{\pi }{2} \right)}{sin\left( x-\frac{\pi }{2} \right)}
\\ \quad \\
\cfrac{cos(x)cos\left(\frac{\pi }{2} \right)+sin(x)sin\left(\frac{\pi }{2} \right)}{sin(x)cos\left(\frac{\pi }{2} \right)-cos(x)sin\left(\frac{\pi }{2} \right)}\implies
\cfrac{cos(x)\cdot 0+sin(x)\cdot 1}{sin(x)\cdot 0-cos(x)\cdot 1}\implies ?\)

Answer 7

what are you left with?

Answer 8

We are left with sin(x)/-cos(x) which equals -tanx. Oh my gosh I get it thank you so much!

Answer 9

yw