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3. trignometrical ratios,functions and identities — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS3. trignometrical ratios,functions and identities1 Mark
MCQ
In a right angled triangle the hypotenuse is $2 \sqrt 2$ times the perpendicular drawn from the opposite vertex. Then the other acute angles of the triangle are
  • A
    $\frac{\pi }{3}$ & $\frac{\pi }{3}$
  • ✓
    $\frac{\pi }{8}$ & $\frac{3 \pi }{8}$
  • C
    $\frac{\pi }{4}$ & $\frac{\pi }{4}$
  • D
    $\frac{\pi }{5}$ & $\frac{3 \pi }{10}$
✓

Answer

Correct option: B.
$\frac{\pi }{8}$ & $\frac{3 \pi }{8}$
b
$p^2sec^2\theta + p^2cosec^2\theta ={\left( {2\sqrt 2 } \right)^2} p^2$

$\Rightarrow$ $\frac{1}{{{{\sin }^2}\theta \,{{\cos }^2}\theta }}\,\, = \,8$

$sin^22\theta = 1/2 = {\left( {\frac{1}{{\sqrt 2 }}} \right)^2}$

$2\theta = n\pi + \pi /4$

$\theta = n\pi /2 + \pi /8$

for $n = 0$      $\Rightarrow$      $\theta = \pi /8$

for $n=1$      $\Rightarrow$      $\theta = 3\pi /8$

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