If 3sin- 5 cos-5- then the absolute value of 5sin-3cos- is

3sinθ+ 5 cosθ=5 ...(1) Let 5sinθ 3cosθ=k ...(2) Squaring equation (1) and (2), and add them ⇒ 34sin^2θ+34cos^2θ=25+k^2 ⇒ 34=25+k^2 ⇒ k^2=9 ⇒ |k|=3 nbsp; ...

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Standard XII

Mathematics

Basic Trigonometric Identities

If 3sinθ+ 5 c...

Question

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

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Solution

$3 sin θ + 5 cos θ = 5 . . . (1)$
Let $5 sin θ - 3 cos θ = k . . . (2)$
Squaring equation $(1)$ and $(2)$ , and add them
$\Rightarrow 34 {sin}^{2} θ + 34 {cos}^{2} θ = 25 + k^{2}$
$\Rightarrow 34 = 25 + k^{2}$
$\Rightarrow k^{2} = 9$
$\Rightarrow | k | = 3$

Absolute value of $5 sin θ - 3 cos θ$ is $3.$

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If 3sinθ+5cosθ=5, then the absolute value of 5sinθ−3cosθ is

3sinθ+5cosθ=5 ...(1) Let 5sinθ−3cosθ=k ...(2) Squaring equation (1) and (2), and add them ⇒34sin2θ+34cos2θ=25+k2 ⇒34=25+k2 ⇒k2=9 ⇒|k|=3 Absolute value of 5sinθ−3cosθ is 3.

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