COMEDK · Maths · 23. Inverse Trigonometric Functions
Evaluate : \(\cos ^{-1}\left[\cos \left(-680^{\circ}\right)\right]+\sin ^{-1}\left[\sin \left(-600^{\circ}\right)\right]-\cos ^{-1}\left(\sin 270^{\circ}\right)\)
- A \(\pi\)
- B \(\dfrac{14 \pi}{9}\)
- C \(-\dfrac{4 \pi}{9}\)
- D \(-\dfrac{5 \pi}{9}\)
Answer & Solution
Correct Answer
(C) \(-\dfrac{4 \pi}{9}\)
Step-by-step Solution
Detailed explanation
The expression is \(E = \cos^{-1}(\cos(-680^{\circ})) + \sin^{-1}(\sin(-600^{\circ})) - \cos^{-1}(\sin 270^{\circ})\). First, simplify the angles: \(\cos(-680^{\circ}) = \cos(680^{\circ}) = \cos(720^{\circ} - 40^{\circ}) = \cos(-40^{\circ}) = \cos(40^{\circ})\). Since…
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