Question
 If sin θ = 3/5 and cos θ = 4/5, find the value of
(2tan² θ + 3cot² θ).Solution
Given: sin θ = 3/5, cos θ = 4/5, First, let's calculate tan θ and cot θ. tan θ = sin θ / cos θ = (3/5) / (4/5) = 3/4, cot θ = 1 / tan θ = 4/3. Now, substitute into the expression: 2tan² θ + 3cot² θ = 2(3/4)² + 3(4/3)² = 2(9/16) + 3(16/9) = 18/16 + 48/9 = 9/8 + 16/3 To add these, take the LCM of 8 and 3, which is 24: = (9×3)/24 + (16×8)/24 = 27/24 + 128/24 = 155/24 ≈ 6.46
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