Question

Show that
Cos2A - Sin2A = - 7/13
Given TanA = 2/3
DO NOT CALCULATE THE VALUE OF A

Answer 1

Answer:-7/13

Step-by-step explanation:

Given that, TanA=2/3=p/b

Now, Cos2A-Sin2A=?

Cos2A=(1-tan^2A)/(1+tan^2A)

={1-(4/9)}/{1+(4/9)}

=(5/9)/(13/9)=5/13

Now Sin2A=2tanA/(1+tan^2A)

=2×(2/3)/{1+(4/9)}

=(4/3)/(13/9)=12/13

Now Cos2A-Sin2A=(5/13)-(12/13)=-7/13