If $a=\sin 175^{\circ}+\cos 175^{\circ}$, then

If $a=\sin 175^{\circ}+\cos 175^{\circ}$, then
  1. $a>0$
  2. $a=0$
  3. $a < 0$
  4. $a=1$

Solution

$\begin{aligned} a &=\sin \left(180^{\circ}-5^{\circ}\right)+\cos \left(180^{\circ}-5^{\circ}\right) \\ &=\sin 5^{\circ}-\cos 5^{\circ} \end{aligned}$ In first quadrunt, $\sin \theta < \sin \theta < \cos \theta$ When $0 \leq \theta < 45^{\circ}$ $\therefore \sin 5^{\circ} < \cos 5^{\circ} \Rightarrow \sin 5^{\circ}-\cos 5^{\circ} < 0 \Rightarrow a < 0$

Asked in: MHT CET 2020 (16 Oct Shift 2)

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