Trigonometric EquationMedium
Question
Total number of integral values of ′n′ so that sin x (sin x + cos x ) = n has at least one solution is -
Options
A.2
B.1
C.3
D.zero
Solution
sin x (sin x + cos x) = n
sin2x + sin x cos x = n
= n ⇒ sin2x - cos2x = 2n -1
⇒ - √2 ≤ 2n - 1 ≤ √2 ⇒
≤ n ≤ 
n = 0, 1
sin2x + sin x cos x = n
= n ⇒ sin2x - cos2x = 2n -1⇒ - √2 ≤ 2n - 1 ≤ √2 ⇒
≤ n ≤ n = 0, 1
Create a free account to view solution
View Solution FreeMore Trigonometric Equation Questions
Number of ordered pairs (a, x) satisfying the equation sec2( a + 2) x + a2 - 1 = 0; - π < x < π is -...A couple is of moment and the force forming the couple is . If is turned through a right angle, the moment of the couple...The value of the expression √3 cosec 20o - sec 20o is equal to...Which of the following numbers is rational ?...The number of solutions of the pair of equations 2 sin2θ - cos2θ = 0 2 cos2θ - 3 sinθ = 0 in the int...