pls solve its both answers 3 and -3
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Given, 3 sin θ + 5 cos θ = 5
(3 sin θ + 5 cos θ) ^2 + (5 sin θ – 3 cos θ)^ 2
= 9 sin^2 θ + 25 cos^2 θ + 30 sin θ cos θ + 25 sin^2 θ + 9 cos^2 θ – 30 sin θ cos θ
= 34 sin^2 θ + 34 cos^2 θ
= 34 (sin^2 θ + cos^2 θ)
= 34 (sin^2 θ + cos^2 θ = 1)
∴ (5)^2 + (5 sin θ – 3 cos θ) ^2 = 34
25 + (5 sin θ – 3 cos θ)^ 2 = 34
(5 sin θ – 3 cos θ) ^2 = 34 – 25
(5 sin θ – 3 cos θ) ^2 = 9
5 sin θ – 3 cos θ = ± 3
(3 sin θ + 5 cos θ) ^2 + (5 sin θ – 3 cos θ)^ 2
= 9 sin^2 θ + 25 cos^2 θ + 30 sin θ cos θ + 25 sin^2 θ + 9 cos^2 θ – 30 sin θ cos θ
= 34 sin^2 θ + 34 cos^2 θ
= 34 (sin^2 θ + cos^2 θ)
= 34 (sin^2 θ + cos^2 θ = 1)
∴ (5)^2 + (5 sin θ – 3 cos θ) ^2 = 34
25 + (5 sin θ – 3 cos θ)^ 2 = 34
(5 sin θ – 3 cos θ) ^2 = 34 – 25
(5 sin θ – 3 cos θ) ^2 = 9
5 sin θ – 3 cos θ = ± 3
ishwarsinghdhaliwal:
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