# If $A \sin \theta=3$ and $A \cos \theta=4$ then &#39; $\theta$ &#39; will be-

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If $A \sin \theta=3$ and $A \cos \theta=4$ then ' $\theta$ ' will be-

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Given that

$Asinθ = 3$

⇒  $sinθ = 3/A$ ... (1)

Also,

$Acosθ = 4$

⇒ $cosθ = 4/A$ ... (2)

Squaring (1) and (2), and adding them both we get

$sin^2θ + cos^2θ = \frac{9}{A^2} + \frac{16}{A^2} = \frac{25}{A^2}$

⇒ $1 = \frac{25}{A^2}$

⇒ $A = 5$

Putting Value of $A$ in (1), we get

$sinθ = \frac{3}{5}$

⇒ $θ = 37°$