Thanks a lot!
Actually the third one i got, it was relatively easy. may i please have help with the others? thanks
1. Multiplying the LHS by $\displaystyle \frac{1+\sin{\theta}}{1+\sin{\theta}}$ gives:
$\displaystyle \frac{\cos{\theta}(1+\sin{\theta})}{1-\sin^2{\theta}} $
Recall that $\displaystyle \sin^2{\theta} + \cos^2{\theta} = 1$
$\displaystyle \frac{\cos{\theta}(1+\sin{\theta})}{\cos^2{\theta} } = \frac{1+\sin{\theta}}{\cos{\theta}}$
Something similar can be done to the RHS.
2. $\displaystyle \cos{\theta}\cot{\theta} $
$\displaystyle = \cos{\theta} \frac{\cos{\theta}}{\sin{\theta}} = \frac{\cos^2{\theta}}{\sin{\theta}} = \frac{1-\sin^2{\theta}}{\sin{\theta}}$
Now simply split and simplify, and you're done.
3 is too easy. Recall that $\displaystyle \tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}}$