Q4 of 23 Page 1

Solve Question:

Eliminate θ, if


x = 3 cosec + 4 cot θ,


y = 4 cosec θ - 3 cot θ.

x = 3 cosec + 4 cot , - - - - - 1

y = 4 cosec - 3 cot . - - - - - 2


Multiply 1 by 4 and 2 by 3


4x = 12cosecθ + 16cotθ


3y = 12cosecθ - 9cotθ


Subtracting


⇒ 4x - 3y = 12cosecθ + 16cotθ - 12cosecθ + 9cotθ


⇒ 4x - 3y = 25cotθ



Re substitute in 1








We know


⇒ Cosec2θ –Cot2θ = 1


∴ square and subtract 3 and 4



⇒ (3x + 4Y)2 - (4x - 3y)2 = 625


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