Question

Prove that (cot A– cos A) / cot A+cos A = (cosec A–1) / (cosec A+1)

Answer 1

Answer:

hope the answer is correct

Answer 2

Proved that (cot A– cos A) / cot A+cos A = (cosec A–1) / (cosec A+1)

Solution:

Need to prove that (cot A – cos A) / ( cot A + cos A ) = (cosec -1 ) / ( cosec + 1)

Let’s solve L.H.S

$\frac{\cot A-\cos A}{\cot A+\cos A}$

We know that $\cot A=\frac{\cos A}{\sin A}$

$= \frac{\frac{\cos A}{\sin A}-\cos A}{\frac{\cos A}{\sin A}+\cos A}$

$= \frac{\cos A\left(\frac{1}{\sin A}-1\right)}{\cos A\left(\frac{1}{\sin A}+1\right)}$

We know that $\frac{1}{sin A} = cosec A$

$= \frac{cosec A-1}{cosec A + 1}$

So L.H.S = R.H.S

Hence proved that (cot A– cos A) / cot A+cos A = (cosec A–1) / (cosec A+1)