Homework Sourse21 Cos X T an2 x2 1Solutionprove 2 1 cos x tan2 x2
2/1 + Cos X - T an^2 x/2 = 1![2/1 + Cos X - T an^2 x/2 = 1Solutionprove ( 2 / 1 + cos x ) - tan2 x/2 = 1 LHS: [ from 1+cos x = 2*cos2 (x/2) , tan (x/2) = sin ( x/2) / cos ( x/2) ] ( 2 / 1 +](/WebImages/9/21-cos-x-t-an2-x2-1solutionprove-2-1-cos-x-tan2-x2-1000462-1761515301-0.webp "2/1 + Cos X - T an^2 x/2 = 1Solutionprove ( 2 / 1 + cos x ) - tan2 x/2 = 1 LHS: [ from 1+cos x = 2*cos2 (x/2) , tan (x/2) = sin ( x/2) / cos ( x/2) ] ( 2 / 1 +")
Solution
prove ( 2 / 1 + cos x ) - tan2 x/2 = 1
LHS:
[ from 1+cos x = 2*cos2 (x/2) , tan (x/2) = sin ( x/2) / cos ( x/2) ]
( 2 / 1 + cos x ) - tan2 x/2
( 2 / 2*cos2(x/2) ) - sin2(x/2) / cos2 (x/2)
[ 1/ cos2(x/2)] - [ sin2(x/2) / cos2 (x/2))
1 - sin2(x/2) / cos2(x/2)
cos2(x/2) / cos2(x/2) ( from sin2 ( x/2) + cos2(x/2) = 1)
= 1
LHS = RHS
