To solve this equation, we can use the trigonometric identity:
sin(A-B) - sin(A+B) = 2cosBsinA
Given:
A = π/6B = x
Therefore, the equation becomes:
2cos(x)sin(π/6) = √2
Using the values of sin(π/6) = 1/2 and cos(π/6) = √3/2, the equation simplifies to:
2(√3/2)sin(x) = √2√3sin(x) = √2sin(x) = √2/√3sin(x) = √6/3
Therefore, the solution to the equation sin(π/6-x)-sin(π/6+x) = √2 is sin(x) = √6/3.
To solve this equation, we can use the trigonometric identity:
sin(A-B) - sin(A+B) = 2cosBsinA
Given:
A = π/6
B = x
Therefore, the equation becomes:
2cos(x)sin(π/6) = √2
Using the values of sin(π/6) = 1/2 and cos(π/6) = √3/2, the equation simplifies to:
2(√3/2)sin(x) = √2
√3sin(x) = √2
sin(x) = √2/√3
sin(x) = √6/3
Therefore, the solution to the equation sin(π/6-x)-sin(π/6+x) = √2 is sin(x) = √6/3.