Question

plse give me anwer for this question
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Answer 1

Question :

      Simplify : sin⁴θ + cos⁴θ

Solution :

Now, sin⁴θ + cos⁴θ

  = (sin²θ)² + (cos²θ)²

  = (sin²θ)² + (cos²θ)²

  = (sin²θ + cos²θ)² - 2 sin²θ cos²θ

  = 1² - 2 sin²θ cos²θ

  = 1 - 2 sin²θ cos²θ

Identity Laws :

  • sin²A + cos²A = 1

  • sec²A - tan²A = 1

  • cosec²A - cot²A = 1

  • (a + b)² = a² + 2ab + b²

  • a² + b² = (a + b)² - 2ab

  • (a - b)² = a² - 2ab + b²

  • a² + b² = (a - b)² + 2ab

Answer 2

sin⁴θ + cos⁴θ

= ( sin²θ )² + ( cos²θ )²

= ( sin²θ + cos²θ )² - 2sin²θcos²θ

[ • Using identity , a² + b² = ( a + b )² - 2ab ]

= 1² - 2sin²θcos²θ

= 1 - 2sin²θcos²θ [ • Required Answer ]

[ • We know , sin²θ + cos²θ = 1 ]