Question
If cos(2θ) = 1 - 2sin²(θ) and tan(θ) + cot(θ) = k,
find the value of k when sin(θ) = 3/5.Solution
We are given sin(θ) = 3/5. Now, find cos(θ): Using the Pythagorean identity: cos(θ) = √(1 - sin²(θ)) = √(1 - (3/5)²) = √(1 - 9/25) = √(16/25) = 4/5. tan(θ) = sin(θ) / cos(θ) = (3/5) / (4/5) = 3/4. cot(θ) = 1 / tan(θ) = 4/3. tan(θ) + cot(θ) = (3/4) + (4/3). = 9/12 + 16/12 = 25/12. Thus, the value of k is 25/12
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