Question
If 4cos²A + 5sin²A = 4.5, then find the value of (sec²A - 1)
Solution
4cos²A + 5sin²A = 4.5
Or, -1cos²A + 5(cos²A + sin²A) = 4.5
Or, -cos²A + 5 = 4.5 (Using cos²A + sin²A = 1)
Or, -cos²A = -0.5 => cos²A = 0.5
So, sec²A = 1/0.5 = 2
Required value = 2 - 1 = 1
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