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Introduction of Trigonometry and its Application — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsIntroduction of Trigonometry and its Application1 Mark
MCQ
Choose the correct answer from the given four options.
The value of the expression $\Big[\frac{\sin^222^\circ+\sin^268^\circ}{\cos^222^\circ+\cos^268^\circ}+\sin^263^\circ+\cos63^\circ\sin27^\circ\Big]$ is:
  • A
    3
  • ✓
    2
  • C
    1
  • D
    0
✓

Answer

Correct option: B.
2
Given expression, $\frac{\sin^222^\circ+\sin^268^\circ}{\cos^222^\circ+\cos^268^\circ}+\sin^263^\circ+\cos63^\circ\sin27^\circ$$=\frac{\sin^222^\circ+\sin^2(90^\circ-22^\circ)}{\cos^2(90^\circ-68^\circ)+\cos^268^\circ}+\sin^263+\cos63^\circ\sin(90^\circ-63^\circ)$
$=\frac{\sin^222^\circ+\cos^222^\circ}{\sin^268^\circ+\cos^268^\circ}+\sin^263^\circ+\cos63^\circ.\cos63^\circ$ $\begin{bmatrix}\because\ \sin(90^\circ-\theta)=\cos\theta \\\text{and }\cos(90^\circ-\theta)=\sin\theta \end{bmatrix}$
$=\frac{1}{1}+(\sin^263^\circ+\cos^263^\circ)$ $[\because\sin^2\theta+\cos^2\theta=1]$
$=1+1=2$

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