Question

Cosec tita+cot tita =k then find cos tita =ksq-1/ksq+1

Answer 1

Answer: $cos = \frac{k^2-1}{k^2+1}$

Step-by-step explanation:

  cosec + cot = k

     $\frac{1}{sin} + \frac{cos}{sin} = k\\\\1+cos = ksin\\\\(1+cos)^2 = (ksin)^2\\\\1 + 2cos +cos^2 = k^2sin^2\\\\1 + 2cos +cos^2 = k^2(1-cos^2)\\\\(1+k^2)cos^2+2cos + 1-k^2 = 0$

Let us solve this quadratic equation

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

or

$cos = \frac{-b-\sqrt{D} }{2a} =\frac{-2-2k^2}{2(k^2+1)} =-1$

but if cos = -1 then sin=0 and cosec = 1/sin cannot exist as given in equation.

so

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

Answer 2

Answer:

your answer attached in the photo