Given that $\sin \theta = \frac{a}{b},$ then $\cos \theta$ is equal to

  • A
    $\frac{b}{\sqrt{b^{2}-a^{2}}}$
  • B
    $\frac{b}{a}$
  • C
    $\frac{a}{\sqrt{b^{2}-a^{2}}}$
  • D
    $\frac{\sqrt{b^{2}-a^{2}}}{b}$

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$2 \sin ^{2} 30^{\circ} \cot 30^{\circ}-3 \cos ^{2} 60^{\circ} \sec ^{2} 30^{\circ} = \dots$

If $4 \tan \theta = 3,$ then $\left(\frac{4 \sin \theta - \cos \theta}{4 \sin \theta + \cos \theta}\right)$ is equal to

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