Question

Srinath, a former Indian cricket player gave a trigonometric question in which sinα + tanα = p and tanα - sinα = q to Kapil Dev. Then calculate the value of p²- q² for Kapil? 

1. 2q√p 
2. 2p√q 
3. pq²
4. 4√pq 

Answer 1

Correct Answer - Option 4 : 4√pq 

Given∶

sinα + tanα = p

tanα - sinα = q

Formula Used∶ 

Basics of Trigonometry; sin²θ + cos²θ = 1

Algebraic Identities ; (a+b)² = a²+ 2ab + b²

(a - b)²= a² - 2ab + b² 

Calculation∶

It is given that,

tanα + sinα = p

tanα - sinα = q

Then, p²- q² = (tanα + sin α)² - (tan α - sin α)²

⇒ tan²α + 2tanα sinα + sin²α - tan²α + 2tanα sinα - sin²α

⇒ 4tanα sinα

⇒ 4√tan²α sin²α 

⇒ 4√tan²α.sin²α

⇒ 4√tan²α .(1- cos²α)

⇒ 4√tan²α - tan²α cos²α

⇒ 4√tan2α - sin2α

⇒ 4√(tanα + sinα) (tan α - sinα)

⇒ 4√pq

∴ The correct option is (4).