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Trigonometry

Trigonometric Identities

jee_main_2026_jan_22_shift_1

Grade None

Question:

If \(\cos \theta = \frac{5}{13}\) and \(\theta\) is acute, find \(\tan \theta\).

Step-by-Step Solution

Key Concept: Use sin²θ + cos²θ = 1.

Step 1: sin²θ = 1 - (5/13)² = 1 - 25/169 = 144/169 => sin θ = 12/13. Step 2: tan θ = sin θ/cos θ = (12/13)/(5/13) = 12/5.

Correct Answer: 12/5

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