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If 3 + 5 =5, then the value of 5 -3 are

Question

If $3 sin θ + 5 cos θ = 5$ , then the value of $5 sin θ - 3 cos θ$ are

\pm 3

\pm 4

\pm 5

\pm 6

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3 sin θ + 5 cos θ = 5

, then the value of

5 sin θ - 3 cos θ

are

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Text solutionVerified

Given

3 sin θ + 5 cos θ = 5

Let

5 sin θ - 3 cos θ = x

Square and add both equations ;

\Rightarrow 9 (sin^{2} θ + cos^{2} θ) + 25 (sin^{2} θ + cos^{2} θ) + 30 sin θ cos θ - 30 sin θ cos θ = 25 + x^{2}

\Rightarrow 9 + 25 = 25 + x^{2}

\Rightarrow x^{2} = 9

\Rightarrow x = \pm 3

\Rightarrow 5 sin θ - 3 cos θ = \pm 3

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Question Text	If $3 sin θ + 5 cos θ = 5$ , then the value of $5 sin θ - 3 cos θ$ are
Answer Type	Text solution:1
Upvotes	150