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Mathematics · 2025 · 3 marks
CBSE 2025 · Region 6 · Set 1 · Q31
In the adjoining figure, TP and TQ are tangents drawn to a circle with centre O. If ∠ OPQ =15^° and ∠ PTQ =θ, then find the value of sin 2 θ.
In the adjoining figure, TP and TQ are tangents drawn to a circle with centre O . If $\displaystyle \angle \mathrm{OPQ}=15^{\circ}$ and $\displaystyle \angle \mathrm{PTQ}=\theta$, then find the value of $\displaystyle \sin 2 \theta$.
Marking-scheme solution
\[\begin{aligned}
& \angle \mathrm{QPT}=75^{\circ} \\
& \angle \mathrm{PQT}=75^{\circ} \\
& \theta=30^{\circ} \\
& \sin 2 \theta=\sin 2\left(30^{\circ}\right) \\
& \quad=\sin 60^{\circ}=\frac{\sqrt{3}}{2}
\end{aligned}
\]
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CBSE Class 10 Mathematics past-paper question from the 2025 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.