CBSE 2025 · Region 4 · Set 1 · Q24 · 2 marks
Find the value of $\displaystyle x$ for which \[(\sin \mathrm{A}+\operatorname{cosec} \mathrm{A})^{2}+(\cos \mathrm{A}+\sec \mathrm{A})^{2}=x+\tan ^{2} \mathrm{~A}+\cot ^{2} \mathrm{~A} \]Evaluate the following : \[\frac{3 \sin 30^{\circ}-4 \sin ^{3} 30^{\circ}}{2 \sin ^{2} 50^{\circ}+2 \cos ^{2} 50^{\circ}} \]
Find the value of $\displaystyle x$ for which \[(\sin \mathrm{A}+\operatorname{cosec} \mathrm{A})^{2}+(\cos \mathrm{A}+\sec \mathrm{A})^{2}=x+\tan ^{2} \mathrm{~A}+\cot ^{2} \mathrm{~A} \]
Evaluate the following : \[\frac{3 \sin 30^{\circ}-4 \sin ^{3} 30^{\circ}}{2 \sin ^{2} 50^{\circ}+2 \cos ^{2} 50^{\circ}} \]
Marking-scheme solution
\[\begin{aligned}
& (\sin \mathrm{A}+\operatorname{cosec} \mathrm{A})^{2}+(\cos \mathrm{A}+\sec \mathrm{A})^{2}=x+\tan ^{2} \mathrm{~A}+\cot ^{2} \mathrm{~A} \\
& \Rightarrow \sin ^{2} \mathrm{~A}+\operatorname{cosec}^{2} \mathrm{~A}+2+\cos ^{2} \mathrm{~A}+\sec ^{2} \mathrm{~A}+2=x+\tan ^{2} \mathrm{~A}+\cot ^{2} \mathrm{~A} \\
& \Rightarrow 1+2+2+1+\cot ^{2} \mathrm{~A}+1+\tan ^{2} \mathrm{~A}=x+\tan ^{2} \mathrm{~A}+\cot ^{2} \mathrm{~A} \\
& \therefore x=7
\end{aligned}
\]
\[\begin{aligned}
& \frac{3 \sin 30^{\circ}-4 \sin ^{3} 30^{\circ}}{2 \sin ^{2} 50^{\circ}+2 \cos ^{2} 50^{\circ}} \\
& =\frac{3 \times \dfrac{1}{2}-4 \times \dfrac{1}{8}}{2\left(\sin ^{2} 50^{\circ}+\cos ^{2} 50^{\circ}\right)} \\
& =\frac{\dfrac{3}{2}-\dfrac{1}{2}}{2 \times 1} \\
& =\frac{1}{2}
\end{aligned}
\]
Introduction to TrigonometryEvaluating and Proving Trigonometric ExpressionsApplyvery_short_answermedium
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CBSE Class 10 Mathematics past-paper question from the 2025board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.