Answer:
To simplify the expression Sec²θ + Cosec²θ - 10, we can use trigonometric identities. Here's how:
1. Rewrite Sec²θ as 1/Cos²θ and Cosec²θ as 1/Sin²θ.
2. Substitute these values into the expression: 1/Cos²θ + 1/Sin²θ - 10.
3. Find a common denominator for the fractions, which is Cos²θ * Sin²θ.
- The first fraction becomes (Sin²θ + Cos²θ) / (Cos²θ * Sin²θ).
- The second fraction becomes (Cos²θ + Sin²θ) / (Cos²θ * Sin²θ).
4. Combine the numerators of the fractions: (Sin²θ + Cos²θ + Cos²θ + Sin²θ) / (Cos²θ * Sin²θ).
5. Simplify the numerator: (2Sin²θ + 2Cos²θ) / (Cos²θ * Sin²θ).
6. Use the Pythagorean identity Sin²θ + Cos²θ = 1 to simplify the numerator: (2(1)) / (Cos²θ * Sin²θ).
7. Simplify the numerator further to: 2 / (Cos²θ * Sin²θ).
8. Finally, we have the simplified expression: 2 / (Cos²θ * Sin²θ).
In summary, the simplified form of the expression Sec²θ + Cosec²θ - 10 is 2 / (Cos²θ * Sin²θ).
Explanation: