If \(cos x = \frac{3}{5}\), then find the value of sin x - sin3 x.1.

1.	If \(cos x = \frac{3}{5}\), then find the value of sin x - sin3 x.1. 0.4762. 0.2883. 0.3584. 0.389
Answer» Correct Answer - Option 2 : 0.288 Given: Cos x = 3/5 Formula used: Sin x = perpendicular/hypotenuse, Cos x = base/hypotenuse, By Pythagoras theorem, Hypotenuse2 = Perpendicular2 + Base2 Calculation: According to the question: Cos x = 3/5 Base = 3 ⇒ Hypotenuse = 5 Hypotenuse2 = Perpendicular2 + Base2 ⇒ 52 = 32 + Perpendicular2 ⇒ 25 = 9 + Perpendicular2 ⇒ 25 – 9 = Perpendicular2 ⇒ Perpendicular2 = 16 ⇒ Perpendicular = √16 ⇒ Perpendicular2 = √(4 × 4) ⇒ Perpendicular = 4 Now, (Sin x – Sin³ x) ⇒ [(perpendicular/hypotenuse) – (perpendicular/hypotenuse)³] ⇒ [4/5 – (4/5)³] ⇒ [4/5 – 64/125] ⇒ (100 – 64)/125 ⇒ 36/125 = 0.288 ∴ The answer is 0.288.

If \(cos x = \frac{3}{5}\), then find the value of sin x - sin3 x.1. 0.4762. 0.2883. 0.3584. 0.389

Answer» Correct Answer - Option 2 : 0.288

Given:

Cos x = 3/5

Formula used:

Sin x = perpendicular/hypotenuse,

Cos x = base/hypotenuse,

By Pythagoras theorem,

Hypotenuse2 = Perpendicular2 + Base2

Calculation:

According to the question:

Cos x = 3/5

Base = 3

⇒ Hypotenuse = 5

Hypotenuse2 = Perpendicular2 + Base2

⇒ 52 = 32 + Perpendicular2

⇒ 25 = 9 + Perpendicular2

⇒ 25 – 9 = Perpendicular2

⇒ Perpendicular2 = 16

⇒ Perpendicular = √16

⇒ Perpendicular2 = √(4 × 4)

⇒ Perpendicular = 4

Now,

(Sin x – Sin³ x)

⇒ [(perpendicular/hypotenuse) – (perpendicular/hypotenuse)³]

⇒ [4/5 – (4/5)³]

⇒ [4/5 – 64/125]

⇒ (100 – 64)/125

⇒ 36/125 = 0.288

∴ The answer is 0.288.