Question

WILL AWARD MEDAL AND FAN! Can someone please explain step by step how to solve this? This is using double and half angle identities.

Answer 1

Ok, this is going to use the half-angle identity for tangent, which is this:

Answer 2

\[\tan \frac{ A }{ 2 }=\frac{ 1-\cos(A) }{ \sin(A) }\]

Answer 3

In order to find the sin of A we have to set up the triangle in QII, like this:

Answer 4

So the sin of the angle is 3/5.

Answer 5

So we can effectively fill in our half-angle formula for tangent now!

Answer 6

cosA=2cos^2(A/2)-1 from half angle identity.
-4/5=2cos^2(A/2)-1
2cos^2(A/2)=1/5
cos^2(A/2)=1/10
cos(A/2)=root 1/10
tan(A/2)=sin(A/2)/cos(A/2)
=(3/root 10)/(1/root 10)
=3

Answer 7

\[\tan \frac{ A }{ 2 }=\frac{ 1-(\frac{ -4 }{ 5 }) }{ \frac{ 3 }{ 5 } }\]

Answer 8

Doing that math gives us:

Answer 9

\[\frac{ \frac{ 5 }{ 5 } +\frac{ 4 }{ 5 }}{ \frac{ 3 }{ 5 } }\]

Answer 10

\[\frac{ \frac{ 9 }{ 5 } }{ \frac{ 3 }{ 5 } }\]is the same thing as:

Answer 11

\[\frac{ 9 }{ 5 }\times \frac{ 5 }{ 3 }\]The 5's will cancel and 9/3 = 3.

Answer 12

Ok thanks for explaining that in detail

Answer 13

You're welcome! Do you have any more of these!? TY for the medal and fan!

Answer 14

Oops...I actually have to go to work now! Wow! Time flies when you're having fun! I'll be back on later tonight!

Answer 15

Ok :)