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Napier’s Analogy

24.If cot^(-1...

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24.If cot^(-1)((2n)/(pi))>(pi)/(3) n in N then number of values of n is (1) 0 (2) 1 (3) 2 (4) 3

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\sqrt{3} \cos θ + \sin θ = \sqrt{2}

, then general value of θ is
(a)

n π + {(- 1)}^{n} \frac{π}{4}, n \in Z

{(- 1)}^{n} \frac{π}{4} - \frac{π}{3}, n \in Z

n π + \frac{π}{4} - \frac{π}{3}, n \in Z

n π + {(- 1)}^{n} \frac{π}{4} - \frac{π}{3}, n \in Z

\sqrt{3} \cos x + \sin x = \sqrt{2}

, then general value of x is
(a)

n π + {(- 1)}^{n} \frac{π}{4}, n \in Z

{(- 1)}^{n} \frac{π}{4} - \frac{π}{3}, n \in Z

n π + \frac{π}{4} - \frac{π}{3}, n \in Z

n π + {(- 1)}^{n} \frac{π}{4} - \frac{π}{3}, n \in Z

I_{n} = 1 \int 0 ({cos}^{- 1} x)^{n} d x,

I_{4}

4 \sin^{2} x = 1

, then the values of x are
(a)

2 n π \pm \frac{π}{3}, n \in Z

n π \pm \frac{π}{3}, n \in Z

n π \pm \frac{π}{6}, n \in Z

2 n π \pm \frac{π}{6}, n \in Z

4 \sin^{2} θ = 1

, then the values of θ are
(a)

2 n π \pm \frac{π}{3}, n \in Z

n π \pm \frac{π}{3}, n \in Z

n π \pm \frac{π}{6}, n \in Z

2 n π \pm \frac{π}{6}, n \in Z

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