Question

If $\cos A = \frac{1}{2}$, then the value of $\sin^2 A + 2\cos^2 A$ is :

• A. $\frac{3}{2}$
• B. $\frac{5}{4}$
• C. $-1$
• D. $\frac{1}{2}$

Hint:

Using trigonometric identities to simplify the expression before substituting values is highly recommended.
It reduces fractional arithmetic and prevents potential radical calculation mistakes.

Answer 1

The Correct Option is B

Step 1: Identify the angle directly instead of using the identity.
Since $\cos A=\frac12$ is a standard value, we know straightaway that $A=60^\circ$.
Step 2: Bring in the matching sine value.
For $A=60^\circ$, $\sin A=\frac{\sqrt3}{2}$, so $\sin^2A=\frac34$ and $\cos^2A=\frac14$.
Step 3: Substitute into the expression.
\[ \sin^2A+2\cos^2A = \frac34 + 2\left(\frac14\right) = \frac34+\frac24=\frac54 \]
\[ \boxed{\dfrac{5}{4}} \]