Trigonometric Identities

Question

The identity 1 + tan²θ equals

RankGuru · Accepted Answer

1. **Start with Basic Identity**: $\sin^2 	heta + \cos^2 	heta = 1$.
2. **Transformation**: Divide the entire equation by $\cos^2 	heta$.
3. **Divide Term-wise**:
   - $\frac{\sin^2 	heta}{\cos^2 	heta} + \frac{\cos^2 	heta}{\cos^2 	heta} = \frac{1}{\cos^2 	heta}$.
4. **Apply Definitions**:
   - $	an^2 	heta + 1 = \sec^2 	heta$.
5. **Domain Note**: This identity holds for all $	heta$ where $\cos 	heta 
eq 0$.

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