Question

WILL AWARD MEDAL AND FAN!!! Can someone PLEASE show me how to do these i still don't get it. Working with double and half angle identities. Picture attached below.

Answer 1

sinA=5/13 in the triangle above
Thus, tanA=5/12 you can see it from the triangle also.
The question asks tan(2A)=2*(tanA)/(1-tan^2(A)) from its half angle identity.
so, tan(2A)=2*(5/12)/(1-(5/12)^2)
=(5/6)/(1-(25/144))
=(5/6)/(119/144)
=120/119