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TRIGONOMETRIC FUNCTIONS — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSTRIGONOMETRIC FUNCTIONS1 Mark
MCQ
Choose the correct answer.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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