Question

Show that root 1+ cos alpha/ 1- cos alpha = cosec alpha + cot alpha

Answer 1

Answer:

cot alpha

Step-by-step explanation:

special category

Answer 2

Answer:

Step-by-step explanation:

It is given to us that
$\sqrt{\frac{1+cos\alpha }{1-cos\alpha } }$

Now as we know
$1+cos\alpha = 2 cos^2\frac\alpha2\\1-cos\alpha = 2 sin^2\frac\alpha2$

So by using above information we get
$\sqrt{ \frac{2 cos^2\frac\alpha2}{2 sin^2\frac\alpha2} }\\=cot\frac\alpha2$

So by solving LHS we get $cot\frac\alpha2$

Now when we solve RHS we get
$cosec \alpha + cot \alpha\\\\=\frac{1}{sin \alpha} + \frac{cos \alpha}{sin \alpha}\\\\= \frac{1+cos\alpha}{sin\alpha} \\\\= \frac{2cos^2\frac\alpha2}{2sin\frac\alpha2cos\frac\alpha2} \\\\=cot \frac\alpha2$

As LHS=RHS it is proved.
#SPJ3