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3.Trigonometrical Ratios, Functions and Identities
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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
$\frac{\pi }{3}$ & $\frac{\pi }{3}$
B
$\frac{\pi }{8}$ & $\frac{3 \pi }{8}$
C
$\frac{\pi }{4}$ & $\frac{\pi }{4}$
D
$\frac{\pi }{5}$ & $\frac{3 \pi }{10}$
Solution
$p^2sec^2\theta + p^2cosec^2\theta ={\left( {2\sqrt 2 } \right)^2} p^2$
$\Rightarrow$ $\frac{1}{{{{\sin }^2}\theta \,{{\cos }^2}\theta }}\,\, = \,8$
$sin^22\theta = 1/2 = {\left( {\frac{1}{{\sqrt 2 }}} \right)^2}$
$2\theta = n\pi + \pi /4$
$\theta = n\pi /2 + \pi /8$
for $n = 0$ $\Rightarrow$ $\theta = \pi /8$
for $n=1$ $\Rightarrow$ $\theta = 3\pi /8$
Standard 11
Mathematics
