Question
Prove the following: $\sin ^2 30^{\circ}+\cos ^2 30^{\circ}=\frac{1}{2} \sec 60^{\circ}$
✓
Answer
$ \text { L.H.S. }$
$ =\sin ^2 30^{\circ}+\cos ^2 30^{\circ}$
$ =\left(\frac{1}{2}\right)^2+\left(\frac{\sqrt{3}}{2}\right)^2$
$ =\frac{1}{4}+\frac{3}{4}$
$ =\frac{4}{4}$
$ =\frac{1}{4}=\frac{1}{2} \times \sec 60^{\circ}$
$ =\text { R.H.S. }$
$ =\sin ^2 30^{\circ}+\cos ^2 30^{\circ}$
$ =\left(\frac{1}{2}\right)^2+\left(\frac{\sqrt{3}}{2}\right)^2$
$ =\frac{1}{4}+\frac{3}{4}$
$ =\frac{4}{4}$
$ =\frac{1}{4}=\frac{1}{2} \times \sec 60^{\circ}$
$ =\text { R.H.S. }$
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