If $\tan \theta = 1$,then $\sin \theta \cdot \cos \theta = \dots$

  • A
    $2$
  • B
    $1$
  • C
    $\frac{1}{2}$
  • D
    $\frac{1}{4}$

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If $1+\sin ^{2} \theta=3 \sin \theta \cos \theta,$ then prove that $\tan \theta=1$ or $\frac{1}{2}$.

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If $\cos (\alpha+\beta)=0,$ then $\sin (\alpha-\beta)$ can be reduced to

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