Question

The value of $\sin^2 18^\circ - \cos^2 72^\circ$ is:

• A. $1$
• B. $0$
• C. $\dfrac{1}{4}$
• D. $-1$

Hint:

Always remember that $\cos \theta = \sin(90^\circ - \theta)$ — this helps simplify many trigonometric problems quickly.

Answer 1

The Correct Option is B

Step 1: Recall the trigonometric identity.
We know that $\sin(90^\circ - \theta) = \cos \theta$.

Step 2: Apply the identity to $\cos 72^\circ$.
\[ \cos 72^\circ = \sin(90^\circ - 72^\circ) = \sin 18^\circ \]
Step 3: Substitute into the given expression.
\[ \sin^2 18^\circ - \cos^2 72^\circ = \sin^2 18^\circ - (\sin 18^\circ)^2 \] \[ = \sin^2 18^\circ - \sin^2 18^\circ = 0 \]
Step 4: Conclusion.
Therefore, $\sin^2 18^\circ - \cos^2 72^\circ = 0$.