Which of the following have the same value (a) $\sin 120^{\circ}$ (b) $\cos 930^{\circ}$ (c) $\tan…
Which of the following have the same value
(a) $\sin 120^{\circ}$
(b) $\cos 930^{\circ}$
(c) $\tan 840^{\circ}$
(d) $\cot \left(-1110^{\circ}\right)$
- only (a) and (b)
- All $(a),(b),(c),(d)$
- only $(a)$ and $(c)$
- only $(\mathrm{c})$ and $(\mathrm{d})$
Solution
(a) $\sin 120^{\circ}=\sin \left(90^{\circ}+30^{\circ}\right)=\cos 30^{\circ}=\frac{\sqrt{3}}{2}$
(b) $\cos 930^{\circ}=\cos \left[\left(2 \times 360^{\circ}\right)+210^{\circ}\right]=\cos 210^{\circ}=\cos (180+30)=-\cos 30^{\circ}=-\frac{\sqrt{3}}{2}$
(c) $\tan 840^{\circ}=\tan \left[\left(2 \times 360^{\circ}\right)+120^{\circ}\right]=-\tan 120^{\circ}=-\cot 30^{\circ}=-\sqrt{3}$
(d) $\cot \left(-1110^{\circ}\right)=-\cot 1110^{\circ}=-\cot \left[\left(3 \times 360^{\circ}\right)+30^{\circ}\right]=-\cot 30^{\circ}=-\sqrt{3}$
Asked in: MHT CET 2020 (14 Oct Shift 2)
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