Question

how to solve this problem

Answer 1

2cos²a-1
=2cos²a-(cos²a+sin²a)
=2cos²a-cos²a-sin²a
=cos²a - sin²a

Substituting this in the equation...

$\frac{ {cos}^{2} a - {sin}^{2}a }{sina.cosa} \\ = \frac{ {cos}^{2} a}{cosa.sina} - \frac{ {sin}^{2}a }{cosa.sina} \\ = \frac{cosa}{sina} - \frac{sina}{cosa} \\ = cota - tana$
Hence Proved.

Hope it Helps...
Here,i used (a) instead of (theta)...

Regards,
Leukonov.