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

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 Given A sin θ = 3, A cos θ = 4

⇒ A2sin2θ = 9, A2cos2θ = 16

⇒ A2sin2θ + A2cos2θ = 9 + 16 = 25

⇒ A2(cos2θ + sin2θ) = 25

⇒ A2 = 25 = 52

⇒ A = \(\pm5\)

(A sin θ) (A cos θ) = 3 x 4  = 12

⇒ A2 sin θ cos θ = 12

⇒ \(\frac{A^2}2\times\) 2 sin θ cos θ = 12

⇒ sin 2θ = \(\frac{24}{A^2}=\frac{24}{25}\) 

⇒ 2θ = sin-1\((\frac{24}{25})\)

⇒ θ = \(\frac12\) sin-1\((\frac{24}{25})\)

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