Question

if sec theta + tan theta =k. prove that sin theta =k^2-1/k^2+1.​

Answer 1

Step-by-step explanation:

sec theta + tan theta =k ---(i)

sec ^ 2 theta - tan ^ 2 theta = 1

( sec theta - tan theta ) (sec theta +tan theta) =1

sec theta- tan theta= 1/k ---(ii)

from (i) and (ii)

2sec theta = k+1/k = k^2 +1 /k

sec theta = k^2 +1 / 2k

cos theta = 2k /1+ k^2

sin theta = k^2- 1/ k^ 2+1