We have to verify sin x < 1 / 2 cos x.

sin x < 1 / 2 cos x

=> 2 sin x * cos x < 1

=> sin 2x < 1

But sin 2x can also be equal to 1.

**Note:** Therefore the inequality should be sin...

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We have to verify sin x < 1 / 2 cos x.

sin x < 1 / 2 cos x

=> 2 sin x * cos x < 1

=> sin 2x < 1

But sin 2x can also be equal to 1.

**Note:** Therefore the inequality should be sin x < = 1/2 cos x.

We therefore prove that **sin x < = 1/ 2 cos x.**