if x is equals to a sec theta and Y is equals to B tan theta prove that b square x square minus A square y square is equals to a square b square
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Step-by-step explanation:
x = a secθ AND y = b tanθ
We have to prove b²x² - a²y² = a²b²
L.H.S.
⇒ b²×(a secθ)² - a²×(b tanθ)²
⇒ a²b² sec²θ - a²b² tan²θ
⇒ a²b²(sec²θ - tan²θ)
⇒ a²b²[(1-sin²θ)÷cos²θ]
⇒ a²b²(cos²θ÷cos²θ) [∵ 1-sin²θ = cos²θ]
⇒ ∴ a²b²
R.H.S = a²b²
∴ L.H.S. = R.H.S.
HENCE, PROVED!!
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