If $\triangle ABC$ is right-angled at $C$,then the value of $\cos(A + B)$ is

  • A
    $1$
  • B
    $\frac{1}{2}$
  • C
    $\frac{\sqrt{3}}{2}$
  • D
    $0$

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If $\sin \theta + \cos \theta = p$ and $\sec \theta + \operatorname{cosec} \theta = q,$ then prove that $q(p^2 - 1) = 2p$.

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