In a ABC, right angled at B, if tan C=√3, then find sin^2 C+cos^2 C/1+cot^2 C.

Question

In a ABC, right angled at B, if tan C=√3, then find sin^2 C+cos^2 C/1+cot^2 C.

1. A. 16/3
2. B. 3/4 (Correct answer)
3. C. 3/16
4. D. 4/15

Correct Answer

Option B — 3/4

Detailed Solution & Explanation

The correct answer is $\dfrac{3}{4}$.

Key Points

• $\tan C=\sqrt3\Rightarrow C=60^\circ$.
• Numerator $\sin^2C+\cos^2C=1$; denominator $1+\cot^2C=\csc^2C=\dfrac{1}{\sin^2C}$.
• So the value $=\sin^2C=\sin^2 60^\circ=\dfrac{3}{4}$.