How do you prove that tan(x/2)=(secx)/(secxcscx+cscx) ?
2 Answers
Let
#tan(y) = sec(2y)/(sec(2y)csc(2y) + csc(2y))#
#tany = (1/cos(2y))/(1/(cos(2y)sin(2y)) + 1/sin(2y))#
#tany = (1/cos(2y))/(1/(cos(2y)sin(2y)) + cos(2y)/(cos(2y)sin(2y))#
#tany = ((cos(2y)sin(2y))/cos(2y))/(1 + cos(2y))#
#tany = (sin2y)/(1 + cos(2y))#
#tany = (2sinycosy)/(1 + 2cos^2y - 1)#
#tany = (2sinycosy)/(2cos^2y)#
#tany = siny/cosy#
#LHS = RHS#
As required.
Hopefully this helps!
Please see below.
Explanation:
We know that,
Here,