Question
If 7cos²A + 2sin²A = 6, then find the value of (sec²A - 1)
Solution
7cos²A + 2sin²A = 6
Or, 5cos²A + 2cos²A + 2sin²A = 6
Or, 5cos²A + 2(cos²A + sin²A) = 6
Or, 5cos²A + 2 = 6 (Using, cos²A + sin²A = 1)
Or, 5cos²A = 4
Or, cos²A = 4/5
So, sec²A = 5/4 (sec A is reciprocal of cos A)
Required value = 5/4 - 1 = 1/4
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