Question

If tanA = 4/3, find the value of
2 sin A - 3 cos A/
2 sin A + 3 cos A​

Answer 1

Given,

tan A = 4/3

To Find,

The value of 2 sin A - 3 cos A and 2 sin A + 3 cos A​

Solution,

Since we are given

tan A = 4/3 = Perpendicular/Base

P =4, B= 3

Now, by using the pythagoreous theorem we can find the hypotenuse

H = 5

Now,

2 sin A = 2 × 4/5

3 cos A = 3× 3/5

2sinA - 3cos A = 2×4/5- 3×3/5 =-1/5

2 sinA + 3cos A = 2×4/5+ 3× 3/5 = 17/5

Hence, the value of 2 sin A - 3 cos A and 2 sin A + 3 cos A is -1/5 and 17/5 respectively. ​

Answer 2

We recall that, trigonometric ratios.

Given:  $tan A=\frac{4}{3}$

$tan A=\frac{Perpendicular}{Base}$

Using Pythagoras Theorem,

$Hypotenuse=\sqrt{Perpendicular^2+Base^2}\\=\sqrt{4^2+3^2}\\=\sqrt{16+9}\\=\sqrt{25}\\=5$

$sinA=\frac{Perpendicular}{Hypotenuse}\\=\frac{4}{5}\\cosA=\frac{Base}{Hypotenuse}\\=\frac{3}{5}$

Substitute the value in the given expression,

$2 sin A - 3 cos A=2\times \frac{4}{5}-3\times \frac{3}{5}\\=\frac{8}{5}-\frac{9}{5}\\=\frac{-1}{5}$

$2 sin A +3 cos A=2\times \frac{4}{5}+3\times \frac{3}{5}\\=\frac{8}{5}+\frac{9}{5}\\=\frac{17}{5}$