Let a ,   b ,   c be three non-zero real numbers such that the equation 3 a cos ⁡ x + 2 b sin ⁡ 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

Question

Let a , &#160; b , &#160; c be three non-zero real numbers such that the equation 3 a cos &#8289; x + 2 b sin &#8289; x = c , &#160; x &#8712; - &#960; 2 , &#160; &#960; 2 has two distinct real roots &#945; and &#946; with &#945; + &#946; = &#960; 3 . Then, the value of b a is

Aicharya · Accepted Answer

3 cos &#8289; x + 2 b a sin &#8289; x = c a Now, 3 cos &#8289; &#945; + 2 b a sin &#8289; &#945; = c a &#160; &#8230; i 3 cos &#8289; &#946; + 2 b a sin &#8289; &#946; = c a &#160; &#8230; ii From equations i and ii &#8658; 3 cos &#8289; &#945; - cos &#8289; &#946; + 2 b a sin &#8289; &#945; - sin &#8289; &#946; = 0 &#8658; 3 - 2 sin &#8289; &#945; + &#946; 2 sin &#8289; &#945; - &#946; 2 + 2 b a 2 cos &#8289; &#945; + &#946; 2 sin &#8289; &#945; - &#946; 2 = 0 &#8658; - 3 + 2 3 &#183; b a = 0 &#8658; b a = 1 2 = 0.5

Let a ,   b ,   c be three non-zero real numbers such that the equation 3 a cos ⁡ x + 2 b…

Solution

Let a , &#160; b , &#160; c be three non-zero real numbers such that the equation 3 a cos &#8289; x + 2 b…

Solution

Let a , b , c be three non-zero real numbers such that the equation 3 a cos ⁡ x + 2 b…