Question

if x=5 cos theta and y=5÷cosec theta then x^2+y^2=

Answer 1

let theta be A for simplicity

x=5cosA

y=5/cosecA

we know that,

cosecA=1/SinA

y=5sinA

x²+y²=(5cosA)²+(5sinA)²

x²+y²=25cos²A+25sin²A

x²+y²=25(cos²A+sin²A)

x²+y²=25(1)................................(sin²A+cos²A=1)

x²+y²=25

thus, 25 is your answer

.

Answer 2

Answer:

x=5cosθ,

y=5/cosecθ=5sinθ. (since, 1/cosecθ=sinθ)

so,x²+y²=(5cosθ)²+(5sinθ)²

=25cos²θ+25sin²θ

=25(cos²θ+sin²θ)

=25. (since,cos²θ+sin²θ=1)