Question
Evaluate: 1 + tan²(cos⁻¹x)
Solution
We are given the expression: 1 + tan²(cos⁻¹x) Recall the trigonometric identity: 1 + tan²θ = sec²θ So, 1 + tan²(cos⁻¹x) = sec²(cos⁻¹x) Now use the identity: sec(cos⁻¹x) = 1 / x (since cos⁻¹x gives an angle whose cosine is x) Therefore: sec²(cos⁻¹x) = (1/x)² = 1/x²
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