FindA if (2sinA\2)squared=2
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assuming you mean
(2 sin(A/2))^2 = 2
4 sin^2(A/2) = 2
sin^2(A/2) = 1/2
sin(A/2) = ±1/√2
Now just find all the angles that fit that.
To find the value of A in the equation (2sin(A/2))^2 = 2, we can follow the steps below:
Step 1: Start with the given equation:
(2sin(A/2))^2 = 2
Step 2: Simplify the equation by expanding the square:
4sin^2(A/2) = 2
Step 3: Divide both sides of the equation by 4:
sin^2(A/2) = 1/2
Step 4: Take the square root of both sides to eliminate the square term:
sin(A/2) = ±sqrt(1/2)
Step 5: Now, determine the possible solutions for A/2 by finding the inverse sine (or arcsine) of both sides:
A/2 = arcsin(±sqrt(1/2))
Step 6: Simplify the expression on the right-hand side:
A/2 = ±pi/4 or A/2 = ±3pi/4
Step 7: To find the values of A, multiply both sides by 2:
A = ±pi/2 or A = ±3pi/2
Therefore, the possible values for A that satisfy the given equation are A = pi/2, A = 3pi/2, A = -pi/2, and A = -3pi/2.