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Chapter 8 · Question 6

Evaluate $\sin^2 30^\circ+\cos^2 30^\circ$ .

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Q6

Evaluate $\sin^2 30^\circ+\cos^2 30^\circ$ .

Answer Revealed

Direct Answer:

By the identity

\sin^2A+\cos^2A=1

, the value is

1

. Directly,

(\frac12)^2+(\frac{\sqrt3}{2})^2=\frac14+\frac34=1

.

Simple Explanation

The identity makes it immediate: answer is

1

.

Exam-Ready Structure

Using standard values,

\sin30^\circ=\frac12

and

\cos30^\circ=\frac{\sqrt3}{2}

. Therefore

\sin^2 30^\circ+\cos^2 30^\circ=\frac14+\frac34=1

.

Key Points

By the identity $\sin^2A+\cos^2A=1$ , the value is $1$ .
Use the NCERT formula or theorem carefully.
Write units and final conclusion where applicable.

Related Questions

Define the six trigonometric ratios for an acute angle $A$ in a right triangle.

Show that $\tan A=\frac{\sin A}{\cos A}$ .

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