Question

3 cot theta =4 then find the value of cos square theta minus sin square theta​

Answer 1

Solution :-

3 cot θ = 4

⇒ cot θ = 4/3

On taking its reciprocal

⇒ tan θ = 3/4

⇒ Opposite side ÷ Adjacent side = 3/4

This is a simple case of right angled triangle in which the sides are 3 cm and 4 cm and Hypotenuse is 5 cm.

So, sin θ = Opposite side ÷ Hypotenuse

→ sin θ = 3 ÷ 5

→ sin θ = 3/5

cos θ = Adjacent side ÷ Hypotenuse

→ cos θ = 4 ÷ 5

→ cos θ = 4/5

For finding the value of cos²θ - sin²θ

→ cos²θ - sin²θ = (4/5)² - (3/5)²

→ cos²θ - sin²θ = 16/25 - 9/25

→ cos²θ - sin²θ = 7/25

∴ cos²θ - sin²θ = ⁷/₂₅