Question

if tan theta + cot theta = 2 then the value of tan ^ 2 theta + cot ^ 2theta = ?​

Answer 1

Given:

• tan θ + cot θ = 2

To find:

• Value of tan²θ + cot²θ = ?

Solution:

tan θ + cos θ = 2

Squaring both sides,

⇏ (tanθ + cotθ)² = (2)²

⇏ tan²θ + cos²θ + 2 tan θ cot θ = 4

⇏ tan²θ + cos²θ + 2 = 4

⇏ tan²θ + cos²θ = 4 - 2

⇏ tan²θ + cos²θ = 2

∴ Hence, Value of tan²θ + cos²θ is 2.

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More to know:

Reciprocal Identities:

• cot θ = 1/tan θ

• cosec θ = 1/sin θ

• sec θ = 1/cos θ

Quotient Identities:

• tan θ = sin θ/cos θ

• cot θ = cos θ/sin θ

Pythagorean Identities:

• sin²θ + cos²θ = 1

• tan²θ + 1 = sec²θ

• 1 + cot²θ = cosec²θ