Trigonometric Identities

Question

The identity 1 + cot²θ equals

RankGuru · Accepted Answer

1. **Pythagorean Identity**: $\sin^2 	heta + \cos^2 	heta = 1$.
2. **Transformation**: Divide the entire equation by $\sin^2 	heta$.
3. **Apply Identities**:
   - $\frac{\sin^2 	heta}{\sin^2 	heta} + \frac{\cos^2 	heta}{\sin^2 	heta} = \frac{1}{\sin^2 	heta}$
   - $1 + \cot^2 	heta = \csc^2 	heta$.
4. **Result**: The value is $	ext{cosec}^2 	heta$.

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