The set of all x in - - satisying -4 cos x-1-5 isA- - -4 -5 -4 -5- - -5 -5- 3 -5- -3 -5-5 -5- 3 -5D- -4 -5-5 -5- 4 -5

The correct option is C ( 3π5, π5)∪(π5,3π5) √(5) lt; 4cos x 1 lt; √(5), (1 √(5))4 lt;cos x lt;(1+√(5))4 Here in ( π,π) cos(±π5)=(1+√(5))4 cos(±3π5)=(1 ...

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Standard XII

Mathematics

General Solution of Trigonometric Equation

The set of al...

Question

The set of all $x$ in $(- π, π)$ satisying $| 4 cos x - 1 | < \sqrt{5}$ is

(- π, \frac{- 4 π}{5}) \cup (\frac{4 π}{5}, π)

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(- \frac{4 π}{5}, - \frac{π}{5}) \cup (\frac{π}{5}, \frac{4 π}{5})

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(- \frac{3 π}{5}, - \frac{π}{5}) \cup (\frac{π}{5}, \frac{3 π}{5})

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(- π, - \frac{π}{5}) \cup (\frac{π}{5}, \frac{3 π}{5})

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Solution

The correct option is C $(- \frac{3 π}{5}, - \frac{π}{5}) \cup (\frac{π}{5}, \frac{3 π}{5})$
$- \sqrt{5} < 4 cos x - 1 < \sqrt{5}, \frac{(1 - \sqrt{5})}{4} < cos x < \frac{(1 + \sqrt{5})}{4}$
Here in $(- π, π)$
$cos (\pm \frac{π}{5}) = \frac{(1 + \sqrt{5})}{4} cos (\pm \frac{3 π}{5}) = \frac{(1 - \sqrt{5})}{4}$

From the graph $x \in (- \frac{3 π}{5}, - \frac{π}{5}) \cup (\frac{π}{5}, \frac{3 π}{5})$

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Similar questions

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General Solution of Trigonometric Equation

Standard XII Mathematics

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The set of all x in (−π,π) satisying |4cosx−1|<√5 is

The correct option is C (−3π5,−π5)∪(π5,3π5)−√5<4cosx−1<√5,(1−√5)4<cosx<(1+√5)4 Here in (−π,π) cos(±π5)=(1+√5)4cos(±3π5)=(1−√5)4 From the graph x∈(−3π5,−π5)∪(π5,3π5)

The set of all $x$ in $(- π, π)$ satisying $| 4 cos x - 1 | < \sqrt{5}$ is