1.

If x = a sec θ + b tan θ y = b sec θ + a tan θ then x2 – y2 is equal to(a) 4ab sec θ tan θ (b) a2 – b2 (c) b2 – a2 (d) a2 + b2

Answer»

(b) a2 – b2

x2 – y2 = (a sec θ + b tan θ)2 – (b sec θ + a tan θ)2 

= a2 sec2 θ + 2ab sec θ tan θ + b2 tanθ - (b2 sec2 θ + 2ab sec θ tan θ + a2 tan2 θ)

= (a2 - b2) sec2 θ + (b2 - a2) tan2 θ

= (a2 - b2)(sec2 θ - tan2 θ)

[(∴ a2 - b2 = - (b2 - a2))(∵ sec2 θ - tan2 θ = 1)]

= a2 – b2



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