Question

cos^4x-sin^4x is equal to?
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Answer 1

Answer:

Cos^2x- Sin^2x

Step-by-step explanation:

• Cos^4x - Sin^4x
• = (cos^2x)^2 - (sin^2x)^2
• =(cos^2x + sin^2x) (cos^2x - sin^2x).....{ (a^2-b^2)= (a+b) (a-b)}
• =cos^2x - sin^2x....{cos^2x + sin^2x = 1}

Answer 2

Solution

cos⁴x - sin⁴x

It is in the form of

a⁴ - b⁴ = (a² - b²)(a² + b²)

→ (cos²x - sin²x)(cos²x + sin²x)

Using

• cos²x - sin²x = cos2x

• cos²x + sin²x = 1

→ cos2x(1)

→ cos2x

→ cos⁴x - sin⁴x = cos2x = cos²x - sin²x

★ Answers

cos⁴x - sin⁴x =

• cos2x

• cos²x - sin²x

• 2cos²x - 1

• 1 - 2sin²x

★ Knowledge enhancer

Trigonometric identities

1st identity : sin²A + cos²A = 1

2nd identity : sec²A - tan²A = 1

3rd identity : cosec²A - cot²A = 1