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Introduction of Trigonometry — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsIntroduction of Trigonometry1 Mark
MCQ
$(\cos0^\circ+\sin30^\circ+\sin45^\circ)(\sin90^\circ+\cos60^\circ-\cos45^\circ)=?$
  • A
    $\frac{5}{6}$
  • B
    $\frac{5}{8}$
  • C
    $\frac{3}{5}$
  • ✓
    $\frac{7}{4}$
✓

Answer

Correct option: D.
$\frac{7}{4}$
$(\cos0^\circ+\sin30^\circ+\sin45^\circ)(\sin90^\circ+\cos60^\circ-\cos45^\circ)$
$=\Big(1+\frac{1}{2}+\frac{1}{\sqrt2}\Big)\Big(1+\frac{1}{2}-\frac{1}{\sqrt2}\Big)$
$=\Big(\frac{3}{2}+\frac{1}{\sqrt2}\Big)\Big(\frac{3}{2}-\frac{1}{\sqrt2}\Big)$
$=\Big(\frac{3}{2}\Big)^2-\Big(\frac{1}{\sqrt2}\Big)^2$
$=\frac{9}{4}-\frac{1}{2}$
$=\frac{9-2}{4}$
$=\frac{7}{4}$

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