ધારો કે $\alpha$ અને $\beta$ વાસ્તવિક સંખ્યાઓ છે જેથી $-\frac{\pi}{4} < \beta < 0 < \alpha < \frac{\pi}{4}$. જો $\sin (\alpha+\beta) = \frac{1}{3}$ અને $\cos (\alpha-\beta) = \frac{2}{3}$ હોય,તો $\left(\frac{\sin \alpha}{\cos \beta} + \frac{\cos \beta}{\sin \alpha} + \frac{\cos \alpha}{\sin \beta} + \frac{\sin \beta}{\cos \alpha}\right)^2$ થી નાનો અથવા તેના જેટલો મહત્તમ પૂર્ણાંક શોધો.

  • A
    $1$
  • B
    $5$
  • C
    $6$
  • D
    $7$

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$\sin\,10^o \sin\,30^o \sin\,50^o \sin\,70^o$ ની કિંમત શોધો.

$\sum_{k=0}^4 \sin^2 \left( (2k+1) \frac{\pi}{20} \right) =$

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જો $(1 + \sin A)(1 + \sin B)(1 + \sin C) = (1 - \sin A)(1 - \sin B)(1 - \sin C)$ હોય,તો દરેક બાજુ કોના બરાબર થાય?

કિંમત શોધો: $\cos^2 \left( \frac{\pi}{4} - \beta \right) - \sin^2 \left( \alpha - \frac{\pi}{4} \right)$

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