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Trigonometric Functions — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsTrigonometric Functions1 Mark
MCQ
If $\sin\theta+\text{cosec}\theta=2,$ then $\sin^2\theta+\text{cosec}^2\theta$ is equal to:
  • A
    $1$
  • B
    $4$
  • ✓
    $2$
  • D
    None of these
✓

Answer

Correct option: C.
$2$
$\sin\theta+\text{cosec}\theta=2$
$\Rightarrow\sin\theta+\frac{1}{\sin\theta}=2$
$\Rightarrow\sin^2\theta+1=2\sin\theta$
$\Rightarrow(\sin\theta-1)^2=0$
$\Rightarrow\sin\theta=1$
$\therefore\sin^2\theta+\text{cosec}^2\theta=1+1=2$

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