To simplify the expression, we can use the trigonometric identity sin(π - x) = sin(x) and cos(π/2 - x) = sin(x).
Using these identities, we can rewrite the expression as:
2sin(a)sin(π/2 - a) + 3sin^2(π/2 - a) - 2
Now, we apply the trigonometric identity sin(a)sin(b) = (1/2)(cos(a - b) - cos(a + b)):
2(1/2)(cos(a - π/2 + a)) + 3sin^2(π/2 - a) - 2= 2(1/2)(cos(π/2)) + 3sin^2(π/2 - a) - 2= 1(0) + 3sin^2(π/2 - a) - 2
Next, we use the trigonometric identity sin(π/2 - x) = cos(x):
3cos^2(a) - 2
Therefore, the simplified expression is 3cos^2(a) - 2.
To simplify the expression, we can use the trigonometric identity sin(π - x) = sin(x) and cos(π/2 - x) = sin(x).
Using these identities, we can rewrite the expression as:
2sin(a)sin(π/2 - a) + 3sin^2(π/2 - a) - 2
Now, we apply the trigonometric identity sin(a)sin(b) = (1/2)(cos(a - b) - cos(a + b)):
2(1/2)(cos(a - π/2 + a)) + 3sin^2(π/2 - a) - 2
= 2(1/2)(cos(π/2)) + 3sin^2(π/2 - a) - 2
= 1(0) + 3sin^2(π/2 - a) - 2
Next, we use the trigonometric identity sin(π/2 - x) = cos(x):
3cos^2(a) - 2
Therefore, the simplified expression is 3cos^2(a) - 2.