If sin A = 1/2, then the value of 3 cot² A + 3 is:
Correct: B
Given sin A = 1/2.
We know that sin 30° = 1/2, so A = 30°.
Now substitute A = 30° into the expression 3 cot² A + 3.
We know cot 30° = √3.
So, 3 cot² 30° + 3 = 3(√3)² + 3
= 3(3) + 3
= 9 + 3 = 12.
Alternatively, we can use the identity 1 + cot² A = cosec² A, which means cot² A = cosec² A - 1.
Substitute this into the expression: 3 cot² A + 3 = 3(cosec² A - 1) + 3
= 3 cosec² A - 3 + 3
= 3 cosec² A.
Since sin A = 1/2, then cosec A = 1/sin A = 1/(1/2) = 2.
So, 3 cosec² A = 3(2)² = 3(4) = 12.