Question

If x = 2 sin⁡A+5 cos⁡A and y = 2 cos⁡A-5 sin⁡A, then prove that x^2+y^2 = 29.,​

Answer 1

Answer:

(3sinθ+5cosθ)

2

+(5sinθ+3cosθ)

2

=9(sin

2

θ+cos

2

θ)+25(sin

2

θ+cos

2

θ)

=34

∴(5sinθ−3cosθ)

2

=34−25=9

⇒(5sinθ−3cosθ)=3

Answer 2

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