If tan(90° - A) = √3 , what is sin A ?

Question

If tan(90° - A) = √3 , what is sin A ?

1. A. 1/2 (Correct answer)
2. B. √3/2
3. C. √2/2
4. D. 3/4

Correct Answer

Option A — 1/2

Detailed Solution & Explanation

The correct answer is 1/2.

Key Points

• Use the complementary identity tan(90° − A) = cot A.
• So $\cot A = \sqrt{3}$, which means $\tan A = \dfrac{1}{\sqrt{3}}$ and $A = 30°$.
• Therefore $\sin A = \sin 30° = \dfrac{1}{2}$.

Additional Information

• The complementary pairs to know: $\sin(90° - A) = \cos A$, $\tan(90° - A) = \cot A$, $\sec(90° - A) = \operatorname{cosec} A$.
• Standard values: $\tan 30° = 1/\sqrt{3}$, $\tan 45° = 1$, $\tan 60° = \sqrt{3}$ — recognising $\sqrt{3}$ as a cotangent immediately fixes the angle at 30°.
• $\sqrt{3}/2$ is offered as the distractor for anyone who solves $A = 60°$ by forgetting the complement.

प्रश्न (हिन्दी में)

यदि tan(90° - A) = √3 , तो sin A क्या है?

1. A. 1/2
2. B. √3/2
3. C. √2/2
4. D. 3/4