Question

Question 7 Find the general solution of the equation sin 2x + cos x = 0

Class X1 - Maths -Trigonometric Functions Page 78

Answer 1

sin2x + cosx = 0
use the formula,
sin2A = 2sinA.cosA

=>2sinx.cosx + cosx = 0
=>cosx(2sinx + 1) = 0
here, cosx = 0 or sinx = -1/2

cosx = 0
x = (2n+1)π/2

again,
sinx = -1/2
sinx= -sin(π/6)
sinx = sin(π+π/6)
sinx = sin(7π/6)
Now, use the general solution
sin∅ = sinA
Then, ∅ = nπ + (-1)ⁿA

x = nπ + (-1)ⁿ(7π/6)

Hence, the solutions are
x = (2n+1)π/2 or nπ+(-1)ⁿ(7π/6)