Question

If cosec theta + cot theta = p prove that cos theta = p2-1 / p2 + 1

Answer 1

Step-by-step explanation:

cosec theta + cot theta = p

=> 1/sin theta + cos theta/sin theta = p

=> (1+cos theta)/sin theta = p

=> (1+cos theta)^2/sin^2 theta = p^2

=> (1+cos theta)^2/(1-cos ^2 theta) = p^2

=> (1+cos theta)^2/{(1-cos theta)(1+cos theta)} = p^2

=> (1+cos theta)/(1-cos theta) = p^2

=> {(1+cos theta)+(1-cos theta)}/{(1+cos theta)-(1-cos theta)} = (p^2 + 1)/(p^2 - 1) [Componendo and Dividendo rule]

=> (1+cos theta+1-cos theta)/(1+cos theta-1+cos theta)} = (p^2 + 1)/(p^2 - 1)

=> 2/2cos theta = (p^2 + 1)/(p^2 - 1)

=> cos theta = (p^2-1) / (p^2 + 1)