Question

Prove :
SinQ/1-cosQ + tanQ/1+cosQ = secQ.cosecQ + cotQ

Answer 1

Answer:

Step-by-step explanation:

So, we have $\frac{sen Q}{1 - cos Q} + \frac{tan Q}{1 + cos Q}$ in the left side.

Then, what we do is match the same denominator.

Thus, after computing the calculations we will get:

$\frac{sen Q (1 + cos Q)}{sen^{2}Q } + \frac{tanQ(1 - cos Q)}{sen^{2}Q}$

Since $tanQ = \frac{sen Q}{cos Q}$ we just need to make cancel law and reach the final equation, as you can see in the picture!

Then we get:

$\frac{1}{senQ} + \frac{cosQ}{senQ} + \frac{1}{cosQsenQ}-\frac{cosQ}{cosQsenQ}$

Which is the same as:

$cosec Q + cotan Q + sec Q . cosec Q - cosec Q = sec Q . cosec Q + cotan Q$    

                           

Hence, it is proven.