1. ## Prove that

show that the value of
[{sin^3(pi + theta)}/{cos ^3(pi/2 + theta)}] * [{cos^3(-theta)}/{sin^3(pi- theta)}] * [{tan(2pi-theta)}/{cosec^2theta}] *

[{sec^2 (pi-theta)}/{sin(2pi + theta)}]
is independent of theta

my incomplete soln-
[{sin^3(pi + theta)}/{cos ^3(pi/2 + theta)}]= -sin^3theta / sin^3theta
[{cos^3(-theta)}/{sin^3(pi- theta)}] = cos^3 theta / sin^3 theta

2. Just so that we're clear, are you asking to simplify

$\displaystyle \frac{\sin^3{\left(\pi + \theta\right)}}{\cos^3{\left(\frac{\pi}{2} + \theta\right)}}\cdot \frac{\cos^3{\left(-\theta\right)}}{\sin^3{\left(\pi - \theta\right)}}\cdot \frac{\tan{\left(2\pi - \theta\right)}}{\csc^2{\left(\theta\right)}} \cdot \frac{\sec^2{\left(\pi - \theta\right)}}{\sin{\left(2\pi + \theta\right)}}$

3. Originally Posted by Prove It
Just so that we're clear, are you asking to simplify

$\displaystyle \frac{\sin^3{\left(\pi + \theta\right)}}{\cos^3{\left(\frac{\pi}{2} + \theta\right)}}\cdot \frac{\cos^3{\left(-\theta\right)}}{\sin^3{\left(\pi - \theta\right)}}\cdot \frac{\tan{\left(2\pi - \theta\right)}}{\csc^2{\left(\theta\right)}} \cdot \frac{\sec^2{\left(\pi - \theta\right)}}{\sin{\left(2\pi + \theta\right)}}$

4. I would start by converting everything to sines and cosines, then applying some unit-circle trigonometric identities to simplify...

5. Originally Posted by Prove It
I would start by converting everything to sines and cosines, then applying some unit-circle trigonometric identities to simplify...
as already mentioned i have simplified the first and the second part , 3rd and 4th are posing problem. i can understand that all the thetas will be cancelled out, but how?

6. For starters, convert EVERYTHING to sines and cosines, including the terms with tangents, secants and cosecants.

7. Originally Posted by Prove It
For starters, convert EVERYTHING to sines and cosines, including the terms with tangents, secants and cosecants.
alrite, i have done, but still one sin theta is not cancelling out, i checked it repeatedly.

8. Which one?

9. Originally Posted by Prove It
Which one?
my answer is coming -cossec theta, what to do now, i have to cancel thetas right?