The value of tan(½ cos⁻¹(√5/3)) is:
The value of tan(½ cos⁻¹(√5/3)) is:
- A. (3−√5)/2
- B. (3+√5)/2
- C. √5/3
- D. 2/(3−√5)
Answer: A) (3−√5)/2
Explanation: Let cos⁻¹(√5/3) = θ, so cos θ = √5/3. tan(θ/2) = √((1 − cos θ) / (1 + cos θ)) = √((3 − √5) / (3 + √5)). Rationalizing gives (3−√5)/2.
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