Question

If sina+coseca=3,find the value of sin^2+cosec^2

Answer 1

Solution:

Given That:

→ sin(a) + cosec(a) = 3

Squaring both sides, we get:

→ sin²(a) + cosec²(a) + 2 × sin(a) × cosec(a) = 9

→ sin²(a) + cosec²(a) + 2 = 9 [As sin(a) and cosec(a) are reciprocal of each other]

→ sin²(a) + cosec²(a) = 7

Which is our required answer.

Answer:

• sin²(a) + cosec²(a) = 7

Learn More:

1. Relationship between sides and T-Ratios.

• sin(x) = Height/Hypotenuse
• cos(x) = Base/Hypotenuse
• tan(x) = Height/Base
• cot(x) = Base/Height
• sec(x) = Hypotenuse/Base
• cosec(x) = Hypotenuse/Height

2. Square formulae.

• sin²(x) + cos²(x) = 1
• cosec²(x) - cot²(x) = 1
• sec²(x) - tan²(x) = 1

3. Reciprocal Relationship.

• sin(x) = 1/cosec(x)
• cos(x) = 1/sec(x)
• tan(x) = 1/cot(x)

4. Cofunction identities.

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

5. Even odd identities.

• sin(-x) = -sin(x)
• cos(-x) = cos(x)
• tan(-x) = -tan(x)