Question

if tan 2a=3/4,then find tan a​

Answer 1

Answer:

tan a = 1/2 , 3/2

Step-by-step explanation:

Given that tan 2a = 3/4

We have to find  the value of tan a

Since we know the famous trigonometric formula ,

$tan 2a = 2 \times tan a - tan^{2} a$

$\frac{3}{4} = 2 \times tan a - tan a^{2}$

$3 = 8 \times tan a - 4 \times tan a^{2}$

$4 \times tan a^{2} - 8 \times tan a + 3 = 0$

$4tan^{2} a - 2 tan a-6tana +3 =0$

$2tan a (2 tana -1) - 3(2tana -1) = 0$

$(2 tana -1)   (2tana-3) = 0$

∴ tan a = 1/2   OR   tan a = 3/2