Question

how can i find this help

Answer 1

hope it helps!!


thanks

Answer 2

We know that cosec^2 theta - cot^2 theta = 1.

(cosec theta - cot theta)(cosec theta + cot theta) = 1

(cosec theta - cot theta)(k) = 1

cosec theta - cot theta = 1/k   ---------------- (1)


Given cosec theta + cot theta = k  ----------- (2)


On solving (1) & (2), we get


cosec theta - cot theta = 1/k

cosec theta + cot theta = k
--------------------------------------------

2 cosec theta = k + 1/k

cosec theta = k^2 + 1/2k

We know that sin theta = 1/cosec theta

                                        = 1/k^2 + 1/2k

                                        = 2k/k^2 + 1.


We know that:

$cos theta = \sqrt{1 - sin^2 theta}$

                        $= \sqrt{1 - (\frac{2k}{k^2 + 1})^2 }$

                       $= \sqrt{1 - \frac{4k^2}{(k^2 + 1)^2} }$

                       $\sqrt{ \frac{k^2 + 1 + 2k^2 - 4k^2}{(k^2 + 1)^2} }$

                       $\sqrt{ \frac{k^2 + 1 - 2k^2}{(k^2 + 1)^2} }$

                       $\sqrt{ \frac{(k^2 - 1)^2}{(k^2+1)^2} }$

                       $\frac{k^2 - 1}{k^2 + 1}$


Hope this helps!