Question

Evaluate cos²∅ tan²∅ + tan²∅ sin²∅ in terms of tan ∅

Class 10
Mathematics .

Quality Answer Needed :)​

Answer 1

Given:

• cos²θ tan²θ + tan²θ sin²θ.

Need to find:

• We need to evaluate the given expression in the terms of tanθ.

Solution:

To solve this type of questions, first we need to know the most important trigonometric identities. Here in this question we need only one trigonometric identities, let's know what trigonometric identity we use here to solve this question.

As we know that,

• cos²θ + sin²θ = 1.

« Now, according to the given question,

→ cos²θ tan²θ + tan²θ sin²θ

→ tan²θ(cos²θ + sin²θ)

→ tan²θ(1)

→ tan²θ × 1

→ tan²θ.

∴ The value of cos²θ tan²θ + tan²θ sin²θ is tan²θ.

⠀⠀

Important trigonometric identities:

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

Answer 2

Answer:

→ cos²θ tan²θ + tan²θ sin²θ

→ tan²θ(cos²θ + sin²θ)

→ tan²θ(1)

→ tan²θ × 1

→ tan²θ.