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TRIGONOMETRIC FUNCTIONS — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSTRIGONOMETRIC FUNCTIONS1 Mark
MCQ
Choose the correct answer. If A lies in the second quadrant and $3\tan\text{A}+4=0,$ then the value of $2\cot\text{A}-5\cos\text{A}+\sin\text{A}$ is equal to:
  • A
    $\frac{-53}{10}$
  • ✓
    $\frac{23}{10}$
  • C
    $\frac{37}{10}$
  • D
    $\frac{7}{10}$
✓

Answer

Correct option: B.
$\frac{23}{10}$
Given that, $3\tan\text{A}+4=0,$ A lies in second quadrant
$\therefore\tan\text{A}=\frac{-4}{3}$
$\cos\text{A}=\frac{-3}{5}$ [A lies in second quadrant]
and $\sin\text{A}=\frac{4}{5}$ and $\cot\text{A}=\frac{-3}{4}$
$\therefore2\cot\text{A}-5\cos\text{A}+\sin\text{A}=2\Big(\frac{-3}{4}\Big)-5\Big(\frac{-3}{5}\Big)+\frac{4}{5}\\=\frac{-3}{2}+3+\frac{4}{5}=\frac{-15+30+8}{10}=\frac{23}{10}$
Hence, the correct option is (b).

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