If acotθ + b cosecθ = p and b cot + a cosec = q then p2 - q2 is equal to
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Correct answer: C
Explanation
The correct answer is Option 3 i.e. b2 - a2.
Given:
a cotθ + b cosecθ = p,
b cotθ + a cosecθ = q
Squaring both the equations and then subtracting the second from the first, we have
⇒ (p)2 - (q)2 = (a cotθ + b cosecθ)2 - (b cotθ + a cosecθ)2
⇒ (a2 cot2θ + b2 cosec2θ + 2 a cotθ b cosecθ) - (b2 cot2θ + a2 cosec2θ + 2b cotθ a cosecθ)
⇒ a2 cot2θ + b2 cosec2θ + 2 a cotθ b cosecθ - b2 cot2θ - a2 cosec2θ - 2b cotθ a cosecθ
⇒ a2 cot2θ + b2 cosec2θ - b2 cot2θ - a2 cosec2θ
⇒ -a2(cosec2θ - cot2θ) + b2(cosec2θ - cot2θ) = p2 - q2
⇒ -a2 + b2 = p2 - q2
⇒ p2 - q2 = b2 - a2