The most general value of - satisfying both the equations sin- - 1-2-tan- - 1-3 is n - I

The correct option is A 2nπ + π/6 ...

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Principal Solution of Trigonometric Equation

The most gene...

Question

The most general value of $θ$ satisfying both the equations $sin θ = \frac{1}{2}, tan θ = \frac{1}{\sqrt{3}} i s (n \in I)$

2 n π + \frac{π}{6}

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(b) 2 n π - \frac{7 π}{6}

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(c) 2 n π + \frac{5 π}{6}

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None of these

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Solution

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θ

sin θ = - \frac{1}{2}

tan θ = \frac{1}{\sqrt{3}}

θ

cos θ . cos (\frac{π}{3} + θ) . cos (\frac{π}{3} - θ) = \frac{1}{4}

θ

sin θ = - 1 / 2

tan θ = 1 / \sqrt{3}

x

sin x > \frac{1}{2}

θ

(- \frac{π}{2}, \frac{π}{2})

(1 - tan θ) (1 + tan θ) {sec}^{2} θ + 2^{{tan}^{2} θ} = 0

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