Question

pls help me out in this problem​

Answer 1

sin A+cosecA = 2

Squaring both sides

(sin A+cosecA)² = 2²

sin² A +cosec² A+2sin A. cosecA = 4

1 sin A sin² A+ cosec²A+2sin A. = 4 sin² A +cosec² A =2

Answer 2

Solution:

Given That:

→ sin(x) + cosec(x) = 2

Squaring both sides, we get:

→ sin²(x) + cosec²(x) + 2 × sin(x) × cosec(x) = 2²

We know that sin(x) and cosec(x) are reciprocals of each other. So, the equation becomes:

→ sin²(x) + cosec²(x) + 2 = 4

→ sin²(x) + cosec²(x) = 2

★ Which is our required answer.

Additional Information:

1. Relationship between sides and T-Ratios.

• sin θ = Height/Hypotenuse
• cos θ = Base/Hypotenuse
• tan θ = Height/Base
• cot θ = Base/Height
• sec θ = Hypotenuse/Base
• cosec θ = Hypotenuse/Height

2. Square formulae.

• sin²θ + cos²θ = 1
• cosec²θ - cot²θ = 1
• sec²θ - tan²θ = 1

3. Reciprocal Relationship.

• sin θ = 1/cosec θ
• cos θ = 1/sec θ
• tan θ = 1/cot θ
• cosec θ = 1/sin θ
• sec θ = 1/cos θ
• tan θ = 1/cot θ

4. Cofunction identities.

• sin(90° - θ) = cos θ
• cos(90° - θ) = sin θ
• cosec(90° - θ) = sec θ
• sec(90° - θ) = cosec θ
• tan(90° - θ) = cot θ
• cot(90° - θ) = tan θ

5. Even odd identities.

• sin -θ = -sin θ
• cos -θ = cos θ
• tan -θ = -tan θ