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Trigonometric Ratios of Multiple and Submultiple Angles — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSTrigonometric Ratios of Multiple and Submultiple Angles1 Mark
MCQ
If $\cot(\alpha+\beta)=0,$ then $\sin(\alpha+2\beta)$ is equal to:
  • ✓
    $\sin\alpha$
  • B
    $\cos2\beta$
  • C
    $\cos\alpha$
  • D
    $\sin2\alpha$
✓

Answer

Correct option: A.
$\sin\alpha$
Given:
$\cot(\alpha+\beta)=0$
$\Rightarrow\frac{\cos(\alpha+\beta)}{\sin(\alpha+\beta)}=0$
$\Rightarrow\cos(\alpha+\beta)=0$
$\Rightarrow\alpha+\beta=\frac\pi2$
$\therefore\sin(\alpha+2\beta)=\sin(\alpha+\alpha+\beta)$
$=\sin\alpha$

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