Solve the given triginometric equation analytically
7 sinx - 2 = 3(2 - sin x)
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Priya
To solve the trigonometric equation 7sin(x) - 2 = 3(2 - sin(x)) analytically, we need to simplify and manipulate the equation to isolate the variable x.
Let's simplify and expand both sides of the equation step by step:
7sin(x) - 2 = 3(2 - sin(x))
Distribute the 3 on the right side:
7sin(x) - 2 = 6 - 3sin(x)
Next, let's collect like terms by moving all terms involving sin(x) to one side and all constant terms to the other side:
7sin(x) + 3sin(x) = 6 + 2
Combine the terms on the left side:
10sin(x) = 8
Now, divide both sides of the equation by 10 to solve for sin(x):
sin(x) = 8/10
Sin(x) simplifies to:
sin(x) = 4/5
So, the solution to the given trigonometric equation is sin(x) = 4/5.
If you need the numerical value of x, you can use the inverse sine function (sin^(-1)) to find x.