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Introduction of Trigonometry — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsIntroduction of Trigonometry1 Mark
MCQ
$\frac{\cos^256^\circ+\cos^234^\circ}{\sin^256^\circ+\sin^234^\circ}+3\tan^256^\circ\tan^234^\circ=?$
  • A
    $3\frac{1}2{}$
  • ✓
    $4$
  • C
    $6$
  • D
    $5$
✓

Answer

Correct option: B.
$4$
$\frac{\cos^256^\circ+\cos^234^\circ}{\sin^256^\circ+\sin^234^\circ}+3\tan^256^\circ\tan^234^\circ$
$=\frac{\big\{\cos(90^\circ-34^\circ)\big\}^2+\cos^234^\circ}{\big\{\sin(90^\circ-34^\circ)\big\}^2+\sin^234^\circ}$
$\ +3\big\{\tan(90^\circ-34^\circ)\big\}^2\tan^234^\circ$
$=\frac{\sin^234^\circ+\cos^234^\circ}{\cos^234^\circ+\sin^234^\circ}+3\cot^234^\circ\tan^234^\circ$ $\begin{bmatrix}\because\cos(90^\circ-\theta)=\sin\theta,\sin(90^\circ-\theta)\\=\cos\theta\ \text{and }\tan(90^\circ-\theta)=\cot\theta\end{bmatrix}$
$=\frac{1}{1}+3\times1$
$\Big[\because\cot\theta=\frac{1}{\tan\theta}$ and $\sin^2\theta+\cos^2\theta=1\Big]$
$=4$

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