MHT CET · Maths · Trigonometric Ratios & Identities
Which of the following have the same value
(a) \(\sin 120^{\circ}\)
(b) \(\cos 930^{\circ}\)
(c) \(\tan 840^{\circ}\)
(d) \(\cot \left(-1110^{\circ}\right)\)
- A only (a) and (b)
- B All \((a),(b),(c),(d)\)
- C only \((a)\) and \((c)\)
- D only \((\mathrm{c})\) and \((\mathrm{d})\)
Answer & Solution
Correct Answer
(D) only \((\mathrm{c})\) and \((\mathrm{d})\)
Step-by-step Solution
Detailed explanation
(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) \(\cot \left(-1110^{\circ}\right)=-\cot 1110^{\circ}=-\cot\)\(\left[\left(3 \times 360^{\circ}\right)+30^{\circ}\right]=-\cot 30^{\circ}=-\sqrt{3}\)
(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) \(\cot \left(-1110^{\circ}\right)=-\cot 1110^{\circ}=-\cot\)\(\left[\left(3 \times 360^{\circ}\right)+30^{\circ}\right]=-\cot 30^{\circ}=-\sqrt{3}\)
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