Question

If 3cotA = 4 then find the value of cos^2A - sin^2A​

Answer 1

Let us assume that ABC is a right angled triangle right angled at B
3cot A=4
cot A=(4/3)
(AB/BC)=(4/3)
AC^2=AB^2+BC^2
AC^2=(3)^2+(4)^2
AC^2=9+16
AC^2=25
AC=5
sin^2A=(BC/AC)^2=(3/5)^2=9/25
cos^2A=(AB/AC)^2=(4/5)^2=16/25
Now,
cos^2A-sin^2A=(16/25)-(9/25)
=(16-9)/25
=7/25
For figure u can refer to the attachment given below