In the given figure, $O$ is the centre of the circle. Find the value of $∠ B D C$ .

30^{o}

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45^{o}

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60^{o}

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75^{o}

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Solution

The correct option is A $45^{o}$
In the given figure, $∠ B D C = ∠ B A C$
$\Rightarrow ∠ B D C = 45^{\circ}$ (Angle subtended by an arc in the same segment are equal.)

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{cos}^{2} 75^{o} + {cos}^{2} 45^{o} + {cos}^{2} 15^{o} - {cos}^{2} 30^{o} - {cos}^{2} 60^{o}

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∠ B A D = 30^{o}

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∠ A O C = 120^{\circ}

∠ B D C

({sin}^{2} 30^{o} + {cos}^{2} 30^{o}) - ({sin}^{2} 60^{o} + {cos}^{2} 60^{o}) + ({sin}^{2} 45^{o} + {cos}^{2} 45^{o})

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