Question

3 tan0 = 4, find the value of 4 COS 0 - Sin 0 / 2 COS 0 + sin 0

Answer 1

Answer:-

(Theta is taken as "A".)

Given:

3 tan A = 4

→ tan A = 4/3

We know that,

Tan A = Opposite side/Adjacent side

Hence,

Opposite side = 4

Adjacent side = 3

Using Pythagoras Theorem,

→ (Hypotenuse)² = (Opposite side)² + (Adjacent side)²

→ Hypotenuse = √[(4)² + (3)²]

→ Hypotenuse = √16 + 9

→ Hypotenuse = √25 = 5

Hence,

sin A = opposite side/hypotenuse

→ sin A = 4/5

Cos A = adjacent side/Hypotenuse

→ Cos A = 3/5

→ 4 Cos A - sin A = 4(3/5) - (4/5)

→ 4 Cos A - sin A = (12 - 4)/5

→ 4 Cos A - sin A = 8/5

→ 2 Cos A + sin A = 2(3/5) + (4/5)

→ 2 Cos A + sin A = (6 + 4)/5

→ 2 Cos A + sin A = 10/5

Hence,

(4 Cos A - sin A)/(2 Cos A + sin A) = (8/5)/(10/5)

→ (4 Cos A - sin A)/(2 Cos A + sin A) = 8/5*5/10

→ (4 Cos A - sin A)/(2 Cos A + sin A) = 4/5