Question

Use an identity to solve the equation on the interval [0,2pi) sin x cos x = -1/4 x=

Answer 1

The solution of the given equation is x = 105 °∈ ( 0 , 2pi)

Explanation:

Step(i):-

Given equation is sin x cos x = -1/4

`2(2sinxcosx) = -1`

we know that trigonometry formula

2 sin x cos x = sin 2x

2 ( sin 2 x) = -1

sin2x = -1/2

Step(ii):-

sin2x =
`(-1)/(2) = sin (\pi +(\pi)/(6)`

sin2x = sin 210

2x = 7π/6

2x = 210°

x = 105 °

The solution of the given equation is x = 105 °∈ ( 0 , 2pi)