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Class 12 Inverse Trigonometric Functions · Mcq Single Correct1 Marksbranch_sensitive_simplification

Class 12 Maths · Inverse Trigonometric Functions · Mcq Single Correct #16

For \(\pi<x<3\pi/2\), simplify \(\tan^{-1}\frac{\sqrt{1+\cos x}+\sqrt{1-\cos x}}{\sqrt{1+\cos x}-\sqrt{1-\cos x}}\).

✅ Step-by-Step Solution

Final Answer: Option (A): \(\pi/4-x/2\)
  1. Here x/2∈(π/2,3π/4), so √(1+cos x)=−√2 cos(x/2) and √(1−cos x)=√2 sin(x/2). The quotient is tan(π/4−x/2). That angle lies in (−π/2,−π/4), so arctan returns π/4−x/2.

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