2 cos θ + sec - $2\sqrt{2}$ = 0, where is an acute angle. Find the value of θ.
Answer & explanation
Correct answer: option 4
2 cosθ + secθ - 2√2 = 0
2 cosθ + \(\frac{1}{cosθ}\) - 2√2 = 0
2 cos²θ - 2√2 cosθ + 1 = 0
2 cos²θ - √2cosθ - √2cosθ + 1 = 0
√2cosθ ( √2 cosθ - 1 ) -1 ( √2 cosθ - 1 ) = 0
( √2 cosθ - 1 ) .( √2 cosθ - 1 ) = 0
( √2 cosθ - 1 ) = 0
cosθ = \(\frac{1}{√2}\)
{ cos45º = \(\frac{1}{√2}\)}
So, θ = 45º