Question

If tan x =
$1 \times \frac{1}{3}$
find value of :
$4 { \sin }^{2} x - 3 { \cos }^{2} x + 2$
​

Answer 1

Step-by-step explanation:

Given,

tan x = 1×⅓

tan x = ⅓

Let,

YZ = 1 , XZ = 3 , XY = ?

According to PHYTHAGAROUS THEROM,

(Hypotenuse)² = (opp.side)² + (adj.side)²

(XY)² = (YZ)² + (XZ)²

(XY)² = (1)² + (3)²

(XY)² = 1 + 9

(XY)² = 10

:. XY = √10

Now consider,

Sin x = opp.side/Hypotenuse = YZ/XY =

1/√10

Cos x = adj.side/Hypotenuse = XZ/XY =

3/√10

Now consider,

4Sin²x - 3Cos²x + 2

=> 4(1/√10)² - 3(3/√10)² + 2

=> 4(1/10) - 3(9/10) + 2

=> 4/10 - 27/10 + 2

=> (4-27+20)/(10)

=> -3/10.

I hope it helps you.