If 4tanA=3, then cos
2
A−sin
2
A equals:

Given:
4tanA=3⟹tanA=
4
3
​

Since tanA=
Base
Perpendicular
​
, let Perpendicular=3 and Base=4.

Using Pythagoras theorem, the hypotenuse (H) is:

H=
3
2
+4
2


​
=
9+16

​
=
25

​
=5
Now, determine sinA and cosA:

sinA=
Hypotenuse
Perpendicular
​
=
5
3
​

cosA=
Hypotenuse
Base
​
=
5
4
​

We need to find the value of cos
2
A−sin
2
A:

cos
2
A−sin
2
A=(
5
4
​
)
2
−(
5
3
​
)
2

cos
2
A−sin
2
A=
25
16
​
−
25
9
​
=
25
7
​