Question

If 6tanθ=5 , Prove that 3cosθ-2sinθ/3cosθ+2sinθ = 2/7

Answer 1

Answer:

Step-by-step explanation:

6 tanθ = 5

tan θ = 5/6

But tan θ = Opposite side to θ/Adjacent side to θ.

Using Pythagoras theorem calculate the hypotenuse

Hypotenuse² = Base² + Height²

Hypotenuse² = 6² + 5² = 61

Hypotenuse = √61.

sinθ = Opposite side to θ/Hypotenuse = 5/√61..

Cosθ = Adjacent side to θ/Hypotenuse = 6/√61.

3cosθ-2sinθ/3cosθ+2sinθ

= 3 *6/√61 - 2 * 5/√61 / 3*6/√61 + 2*5/√61

= (18 - 10)/√61 / (18 + 10)/√61

= 8/28 = 2/7

Hence proved.