COMEDK · Maths · 8. Trigonometric Ratios & Identities
The expression \(\dfrac{\tan\left(x - \dfrac{\pi}{2}\right)\cos\left(\dfrac{3\pi}{2} + x\right) - \sin^3\left(\dfrac{7\pi}{2} - x\right)}{\cos\left(x - \dfrac{\pi}{2}\right)\tan\left(\dfrac{3\pi}{2} + x\right)}\) simplifies to:
- A \(\sin^2 x\)
- B \(1 + \cos^2 x\)
- C \(\cos^2 x - \sin^2 x\)
- D \(-(1 + \cos^2 x)\)
Answer & Solution
Correct Answer
(A) \(\sin^2 x\)
Step-by-step Solution
Detailed explanation
We simplify each term in the given expression using trigonometric identities: \(\tan\left(x - \dfrac{\pi}{2}\right) = -\tan\left(\dfrac{\pi}{2} - x\right) = -\cot x\) \(\cos\left(\dfrac{3\pi}{2} + x\right) = \sin x\)…
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