Question

If asec theta - btan theta = 2
then find the value of
bsec theta - atan theta = ?

Answer 1

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Answer 2

value of b secθ - a tanθ is ±√(4 - a² + b²)

given, a secθ - b tanθ = 2 ........(1)

we have to find out the value of b secθ - a tanθ

let b secθ - a tanθ = x .......(2)

squaring and subtracting equations from (1) of (2) we get,

(a secθ - b tanθ)² - (b secθ - b tanθ)² = 2² - x²

⇒a²sec²θ + b²tan²θ -2ab secθ.tanθ - (b²sec²θ + b²tan²θ - 2ab secθ.tanθ) = 2² - x²

⇒a²(sec²θ - tan²θ) - b²(sec²θ - tan²θ) = 4 - x²

⇒a² × 1 - b² × 1 = 4 - x²

⇒x² = 4 - a² + b²

⇒x = ±√(4 - a² + b²)

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