Question

if cosA =3/4 ,then find the value of 9 tan^2 A + 9​

Answer 1

Create ΔABC, then use pythagorean theorem.

(Picture Uploaded)

∴tan A = $\frac{\sqrt{7} }{3}$

Thus, tan² A = $\frac{7}{9}$ .

∴tan² A + 9 = $\frac{88}{9}$

88/9 is the ans.

Answer 2

Step-by-step explanation:

draw a triangle abc where b is 90 degrees

cosA = 3/4

cosA=base/hypotenuse

base = 3 units

hypotenuse=4 units

so by using Pythagorean theorem

(hypotenuse)²=(base)²+(perpindicular)²

4²=3²+x²

16=9+x²

7=xC

√7=x

√7/3=tanA

9 tan²A+9

=9 x (√7/3)²+9

=9 x 7/9 + 9

=7+9

=16