Question

How to verify 10 and 11

Answer 1

10. LHS = tan2x = 2tanx/(1 - tan^2x)
Now, we can divide the LHS by tanx to yield the numerator as 2.

So, 2tanx/tanx/(1 - tan^2x)/tanx
= 2/(1/tanx - tanx)
= 2/(cotx - tanx)

11. LHS = 1 + sin2x/2 = 1 + sinxcosx
Since we want secx on the bottom, we divide by 1/cosx.
(1 + sinxcosx)/(1/cosx) = (secx + sinx)/secx