Question

•If 2ycosθ = xsinθ and 2xsecθ - ycosecθ = 3, then value of x2 + y2 is.

(with process)
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Answer 1

Answer:

4

Step-by-step explanation:

Given:

2ycosθ = xsinθ ; 2xsecθ - ycosecθ = 3

2xsecθ - ycosecθ = 3

2x/cosθ - y/sinθ = 3

2xsinθ - ycosθ = 3sinθ cosθ ..(i)

2ycosθ = xsinθ

ycosθ = xsinθ/2

Substitute ycosθ in (i),

2xsinθ - (xsinθ/2) = 3sinθ cosθ

(4xsinθ - xsinθ)/2 = 3sinθ cosθ

4xsinθ - xsinθ = 6sinθ cosθ

3xsinθ = 6sinθ cosθ

x = 2cosθ

ycosθ = 2cosθsinθ/2

y = sinθ

x2 + y2 = 4cos2θ + sin2θ

= 4(1) (wkt, sin2θ + cos2θ = 1 )

= 4.