જો $\tan \theta = \frac{a}{b}$ હોય,તો $\frac{{\sin \theta }}{{{{\cos }^8}\theta }} + \frac{{\cos \theta }}{{{{\sin }^8}\theta }} = $

  • A
    $\pm \frac{{{{({a^2} + {b^2})}^4}}}{{\sqrt {{a^2} + {b^2}} }}\left( {\frac{a}{{{b^8}}} + \frac{b}{{{a^8}}}} \right)$
  • B
    $\pm \frac{{{{({a^2} + {b^2})}^4}}}{{\sqrt {{a^2} + {b^2}} }}\left( {\frac{a}{{{b^8}}} - \frac{b}{{{a^8}}}} \right)$
  • C
    $\pm \frac{{{{({a^2} - {b^2})}^4}}}{{\sqrt {{a^2} + {b^2}} }}\left( {\frac{a}{{{b^8}}} + \frac{b}{{{a^8}}}} \right)$
  • D
    $\pm \frac{{{{({a^2} - {b^2})}^4}}}{{\sqrt {{a^2} - {b^2}} }}\left( {\frac{a}{{{b^8}}} - \frac{b}{{{a^8}}}} \right)$

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$k$ ની કઈ કિંમત માટે $(\cos x + \sin x)^2 + k \sin x \cos x - 1 = 0$ એ નિત્યસમ બને?

જો $\alpha = 22^\circ 30'$ હોય,તો $(1 + \cos \alpha )(1 + \cos 3\alpha )(1 + \cos 5\alpha )(1 + \cos 7\alpha )$ ની કિંમત શોધો.

એક માણસ $100 \, m$ ઊંચાઈ ધરાવતા ટાવરની ટોચનો ઉત્સેધકોણ $30^{\circ}$ જુએ છે. ટાવર તરફ અમુક અંતર ચાલ્યા પછી,તે ઉત્સેધકોણ $45^{\circ}$ જુએ છે. માણસ ટાવર તરફ કેટલું અંતર ચાલ્યો હશે? ($m$ માં)

Difficult
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જો $\frac{x}{\cos \theta} = \frac{y}{\cos \left( \theta - \frac{2\pi}{3} \right)} = \frac{z}{\cos \left( \theta + \frac{2\pi}{3} \right)},$ હોય,તો $x + y + z = $

$\sin (\beta + \gamma - \alpha ) + \sin (\gamma + \alpha - \beta ) + \sin (\alpha + \beta - \gamma ) - \sin (\alpha + \beta + \gamma ) = $

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