✓ Board-verified↻ asked 3×
Mathematics · 2024 · 2 marks
CBSE 2024 · Region 4 · Set 1 · Q23
Evaluate : $\displaystyle \frac{5 \cos ^{2} 60^{\circ}+4 \sec ^{2} 30^{\circ}-\tan ^{2} 45^{\circ}}{\sin ^{2} 30^{\circ}+\sin ^{2} 60^{\circ}}$If $\displaystyle \sin (\mathrm{A}-\mathrm{B})=\frac{1}{2}, \cos (\mathrm{~A}+\mathrm{B})=\frac{1}{2} ; 0<\mathrm{A}+\mathrm{B} \leq 90^{\circ}, \mathrm{A}>\mathrm{B}$; find $\displaystyle \angle \mathrm{A}$ and $\displaystyle \angle \mathrm{B}$.
Evaluate : $\displaystyle \frac{5 \cos ^{2} 60^{\circ}+4 \sec ^{2} 30^{\circ}-\tan ^{2} 45^{\circ}}{\sin ^{2} 30^{\circ}+\sin ^{2} 60^{\circ}}$
If $\displaystyle \sin (\mathrm{A}-\mathrm{B})=\frac{1}{2}, \cos (\mathrm{~A}+\mathrm{B})=\frac{1}{2} ; 0<\mathrm{A}+\mathrm{B} \leq 90^{\circ}, \mathrm{A}>\mathrm{B}$; find $\displaystyle \angle \mathrm{A}$ and $\displaystyle \angle \mathrm{B}$.
Marking-scheme solution
\[\begin{aligned}
& \frac{5\left(\dfrac{1}{2}\right)^{2}+4\left(\dfrac{2}{\sqrt{3}}\right)^{2}-(1)^{2}}{\left(\dfrac{1}{2}\right)^{2}+\left(\dfrac{\sqrt{3}}{2}\right)^{2}} \\
& =\frac{67}{12}
\end{aligned}
\]
\[\begin{gathered}
\sin (A-B)=\sin 30^{\circ} \\
A-B=30^{\circ} \\
\cos (A+B)=\cos 60^{\circ} \\
A+B=60^{\circ}
\end{gathered}
\]
Solving (i) and (ii)
\[\mathrm{A}=45^{\circ}, \mathrm{B}=15^{\circ}
\]
More from Introduction to Trigonometry
- If sin θ+ cos θ=√3, then prove that tan θ+ cot θ=1 OR Prove that: ( sin A+ sec A)^2+( cos A+cosec A)^2=(1+…2026 · asked 3×
- The hour-hand of a clock is 6 cm long. The angle swept by it between 7:20 a.m. and 7:55 a.m. is:2023 · asked 3×
- If sin θ= cos θ,(0^°<θ<90^°), then value of ( sec θ · sin θ) is:2024 · asked 3×
- Given that sin 2 α=(√3)/2, the value of sin 3 α is:2026 · asked 3×
- Which of the following statements is true?2025 · asked 3×
- Prove that ( sin A-2 sin^3 A)/(2 cos^3 A- cos A)= tan A OR Prove that sec A(1- sin A)( sec A+ tan A)=1.2023 · asked 3×
- If 2 tan A=3, then the value of (4 sin A+3 cos A)/(4 sin A-3 cos A) is2023 · asked 3×
- Evaluate: 2 √2 cos 45^° sin 30^°+2 √3 cos 30^° OR If A=60^° and B=30^°, verify that: sin (A+B)= sin A cos B+…2024 · asked 3×
CBSE Class 10 Mathematics past-paper question from the 2024board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.