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Question
If x = a sec θ + b tan θ and y = a tan θ + b sec θ prove that x2 - y2 = a2 - b2.
Solution
Here,
x2 = a2 sec2θ + 2ab sec θ.tan θ + b2tan2θ
y2 = a2 tan2θ + 2ab sec θ.tan θ + b2sec2θ
⇒ x2 - y2 = a2 ( sec2θ - tan2θ ) - b2 ( sec2θ - tan2θ )
⇒ x2 - y2 = a2 - b2. ....( ∵ sec2θ - tan2θ = 1)
Hence proved.
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