TS EAMCET · Maths · Trigonometric Ratios & Identities
If \(\mathrm{A}+\mathrm{B}+\mathrm{C}=\frac{\pi}{2}\), then \[ \sqrt{2} \cos \left(\frac{\pi}{4}-A\right)+\sqrt{2} \cos \left(\frac{\pi}{4}-B\right)+\sqrt{2} \cos \left(\frac{\pi}{4}-C\right)+1= \]
- A \(4 \sqrt{2} \cos \frac{A}{2} \cos \frac{B}{2} \cos \frac{C}{2}\)
- B \(4 \cos \frac{\mathrm{A}}{2} \cos \frac{\mathrm{B}}{2} \cos \frac{\mathrm{C}}{2}\)
- C \(4 \sin \frac{A}{2} \sin \frac{B}{2} \cos \frac{C}{2}\)
- D \(4 \sqrt{2} \sin \frac{A}{2} \sin \frac{B}{2} \cos \frac{C}{2}\)
Answer & Solution
Correct Answer
(A) \(4 \sqrt{2} \cos \frac{A}{2} \cos \frac{B}{2} \cos \frac{C}{2}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \sqrt{2} \cos \left(\frac{\pi}{4}-\mathrm{A}\right)+\sqrt{2} \cos \left(\frac{\pi}{4}-\mathrm{B}\right)+ \\ & \qquad \sqrt{2} \cos \left(\frac{\pi}{4}-\mathrm{C}\right)+\sqrt{2} \cos \left(\frac{\pi}{4}\right)\end{aligned}\)…
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