If a an b are nonzero constant, simplify {√3 a sin (pi/b)}^2 + {√3 a cos (pi/b)}^2
To simplify the given expression, we can use the trigonometric identity: sin^2(x) + cos^2(x) = 1.
Let's break down the given expression step by step:
Step 1: Expand the expression.
{√3 a sin (π/b)}^2 + {√3 a cos (π/b)}^2
Step 2: Apply the trigonometric identity: sin^2(x) + cos^2(x) = 1.
{√3 a}^2 * sin^2 (π/b) + {√3 a}^2 * cos^2(π/b)
Step 3: Simplify.
3a^2 * sin^2 (π/b) + 3a^2 * cos^2(π/b)
Step 4: Apply the trigonometric identity again: sin^2(x) + cos^2(x) = 1.
3a^2 * 1 + 3a^2 * 1
Step 5: Simplify further.
3a^2 + 3a^2
Step 6: Combine like terms.
6a^2
Therefore, the simplified form of the expression is 6a^2.