If sec ^2 α+4 cos ^2 α=4 and 0^° ≤ α ≤ 90^°, then find the value of α.

4cos²α + \(\frac{1}{cos²α}\)  = 4

4cos⁴α + 1  = 4 cos²α

4cos⁴α - 4 cos²α + 1 = 0

4 cos²α ( cos²α - 1 ) -1 ( cos²α - 1 ) = 0

Now  cos²α - 1 = 0 and 4cos²α - 1 = 0

cos²α - 1 = 0

α = 90º  ( not possible )

4cos²α - 1 = 0

cos²α = \(\frac{1}{4}\)

So , α = 45º