Question

The value of cosec2

(90- ) - tan2 is

a] 1

b] -1

c] 2

d] -2
​

Answer 1

CORRECT QUESTION.

Find the value of cosec²(90° - θ) - tan²θ.

a) 1

b) -1

c) 2

d) -2

ANSWER.

• Option a is the right answer for the question.

SOLUTION.

We know that,

→ cosec(90° - θ) = sec θ

Therefore,

→ cosec²(90° - θ) = sec²θ

Therefore,

cosec²(90° - θ) - tan²θ

= sec²θ - tan²θ

= 1 (Using formula sec²θ - tan²θ = 1)

★ So, option A is the right answer for the question.

ADDITIONAL INFORMATION.

1. Relationship between sides.

• 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.

• sin²x + cos²x = 1.
• cosec²x - cot²x = 1.
• sec²x - tan²x = 1

3. Reciprocal Relationship.

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

4. Co-function identities.

• sin(90° - x) = cos(x) and vice versa.
• cosec(90° - x) = sec(x) and vice versa.
• tan(90° - x) = cot(x) and vice versa.