Trigonometric EquationHard
Question
The least value of $\left( \cos^{2}\theta - 6sin\theta cos\theta + 3\sin^{2}\theta + 2 \right)$ is
Options
A.-1
B.$4 + \sqrt{10}$
C.$4 - \sqrt{10}$
D.1
Solution
$f(\theta) = \frac{1 + cos2\theta}{2} - 3sin2\theta + 3\left( \frac{1 - cos2\theta}{2} \right) + 2$
$${f(\theta) = 4 - 3sin2\theta - cos2\theta }{f(\theta) \in \lbrack 4 - \sqrt{10},4 + \sqrt{10}\rbrack}$$
Create a free account to view solution
View Solution FreeMore Trigonometric Equation Questions
If A and B be acute positive angles satisfying 3 sin2 A + 2 sin2B = 1 and 3 sin2A - 2 sin2B = 0. then-...The equation of the bisector of the acute angle between the lines 2x - y + 4 = 0 and x - 2y = 1 is :-...In triangle ABC, 2ac sin (A - B + C) =...Let α, β be such that π and cos α + cos β = , then the value of cos is...Find all values of θ lying between 0 and 2π satisfying the equation r sin θ = √3 and r + 4 sin _...