If Sin- -3 Cos - 1- - - then the possible values of - - are -

The correct option is D π/6≤θ≤π/2 sinθ +√(3) cosθ⩾ 1 2(sinθ× #10;(1/2)+(√(3)/2)cosθ )⩾ 1 2sin(θ +(π/3))⩾ #10;1 sin(θ +(π/3))⩾(1/2) ...

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Standard XII

Mathematics

Basic Trigonometric Identities

If Sinθ +√3...

Question

If $S i n θ + \sqrt{3} C o s \geq 1, - π < θ \leq π$ then the possible values of ' $θ$ ' are ................

\frac{- π}{3} \leq θ < \frac{2 π}{3}

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\frac{- π}{6} \leq θ \leq \frac{2 π}{2}

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\frac{- π}{4} \leq θ \leq \frac{π}{2}

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\frac{- π}{6} \leq θ \leq \frac{π}{2}

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Solution

The correct option is D $\frac{- π}{6} \leq θ \leq \frac{π}{2}$
$s i n θ + \sqrt{3} c o s θ ⩾ 1 2 (s i n θ \times (\frac{1}{2}) + (\frac{\sqrt{3}}{2}) c o s θ) ⩾ 1 2 s i n (θ + (\frac{π}{3})) ⩾ 1 s i n (θ + (\frac{π}{3})) ⩾ (\frac{1}{2}) (\frac{π}{6}) \leq θ + (\frac{π}{3}) \leq (\frac{5 π}{6}) (\frac{- π}{6}) \leq θ \leq (\frac{π}{2})$

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If Sinθ+√3Cos≥1,−π<θ≤π then the possible values of 'θ' are ................

The correct option is D −π6≤θ≤π2sinθ+√3cosθ⩾12(sinθ×(12)+(√32)cosθ)⩾12sin(θ+(π3))⩾1sin(θ+(π3))⩾(12)(π6)≤θ+(π3)≤(5π6)(−π6)≤θ≤(π2)

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