Let a, b, c be three non-zero real numbers such that the equation √3acos⁡x+2bsin⁡x=c, x∈-(π)/2, (π)/2 has two distinct real roots α and β with…

Question

Let a, b, c be three non-zero real numbers such that the equation √3acos⁡x+2bsin⁡x=c, x∈-(π)/2, (π)/2 has two distinct real roots α and β with α+β=(π)/3. Then, the value of b/a is

MARKS Content Team · Accepted Answer

Correct answer: 0.5. √3cos⁡x+2b/asin⁡x=c/a Now, √3cos⁡α+2b/asin⁡α=c/a …i √3cos⁡β+2b/asin⁡β=c/a …ii From equations i and ii ⇒√3cos⁡α-cos⁡β+2b/asin⁡α-sin⁡β=0 ⇒√3-2sin⁡(α+β)/2sin⁡(α-β)/2+2b/a2cos⁡(α+β)/2sin⁡(α-β)/2=0 ⇒-√3+2√3·b/a=0 ⇒b/a=1/2=0.5

Let $a, b, c$ be three non-zero real numbers such that the equation $\sqrt{3} a \cos x + 2 b \sin x = c, x \in [- \frac{π}{2}, \frac{π}{2}]$ has two distinct real roots $α$ and $β$ with $α + β = \frac{π}{3}$ . Then, the value of $\frac{b}{a}$ is

Solution

More Trigonometric Ratios & Identities Questions

Let a, b, c be three non-zero real numbers such that the equation 3acos⁡x+2bsin⁡x=c, x∈-π2, π2 has two distinct real roots α and β with α+β=π3. Then, the value of ba is

Solution

More Trigonometric Ratios & Identities Questions

Let $a, b, c$ be three non-zero real numbers such that the equation $\sqrt{3} a \cos x + 2 b \sin x = c, x \in [- \frac{π}{2}, \frac{π}{2}]$ has two distinct real roots $α$ and $β$ with $α + β = \frac{π}{3}$ . Then, the value of $\frac{b}{a}$ is