Question

prove that cot teta+tan teta=cosec teta. sec teta​

Answer 1

Required Answer:-

Given To Prove:

• cot θ + tan θ = cosec θ sec θ

Proof:

To prove this, we need to prove LHS = RHS.

We know that,

→ tan θ = sin θ/cos θ and,

→ cot θ = cos θ/sin θ

Taking LHS,

cot θ + tan θ

= cos θ/sin θ + sin θ/cos θ

LCM of sin θ and cos θ is - sin θ cos θ,

= (cos²θ + sin²θ)/(sin θ cos θ)

We know that,

→ sin²θ + cos²θ = 1

→ LHS = 1/(sin θ cos θ)

Reciprocal of sin θ is cosec θ and that of cos θ is sec θ ★

So, LHS,

= cosec θ sec θ

= RHS (Hence Proved)

Basic Trigonometry Formulae:

1. Relationship between sides.

• 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. Quotient Identities.

• tan θ = sin θ/cos θ
• cot θ =cos θ/sin θ

3. Reciprocal Identities.

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

4. Cofunction Identities.

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

5. Pythagoras Identities.

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

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