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Sec²thita + cosec²thita-10

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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:

User Danesh
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