If 3 sin - -4 cos- -5- then the value of tan - is -

Given, 3 sin θ +4 cosθ =5.......(1) nbsp; Squaring both sides, we have: (3 sin θ +4 cosθ)^2 = (5)^2 ⇒ 9 nbsp;sin^2θ +16 cos^2θ + 24 nbsp;sin θ cos ...

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Byju's Answer

Standard X

Mathematics

Complementary Trigonometric Ratios

If 3 sin θ +4...

Question

If $3 s i n θ + 4 c o s θ = 5$ , then the value of $t a n θ$ is _____.

$\frac{2}{3}$

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$\frac{4}{5}$

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$\frac{3}{5}$

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$\frac{3}{4}$

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Solution

The correct option is D
$\frac{3}{4}$

$G i v e n, 3 s i n θ + 4 c o s θ = 5....... (1) S q u a r i n g b o t h s i d e s, w e h a v e : (3 s i n θ + 4 c o s θ)^{2} = (5)^{2} \Rightarrow 9 {sin}^{2} θ + 16 {cos}^{2} θ + 24 s i n θ c o s θ = 25 \Rightarrow 9 (1 - {cos}^{2} θ) + 16 (1 - {sin}^{2} θ) + 24 s i n θ c o s θ = 25 \Rightarrow 9 - 9 c o s^{2} θ + 16 - 16 {sin}^{2} θ + 24 s i n θ c o s θ = 25 \Rightarrow 16 {sin}^{2} θ + 9 c o s^{2} θ - 24 s i n θ c o s θ = 0 \Rightarrow (4 s i n θ - 3 c o s θ)^{2} = 0 \Rightarrow 4 s i n θ - 3 c o s θ = 0$
$\Rightarrow 4 s i n θ = 3 c o s θ$

$\Rightarrow t a n θ = \frac{3}{4}$

Suggest Corrections

If 3sinθ+4cosθ=5, then the value of tanθ is _____.

If $3 s i n θ + 4 c o s θ = 5$ , then the value of $t a n θ$ is _____.