If sin θ – cos θ = 0, then the value of sin⁴ θ + cos⁴ θ is
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Given: sinθ – cosθ = 0.
1. Solve for θ:
sinθ = cosθ ⇒ tanθ = 1 ⇒ θ = 45°.
2. For θ = 45°:
sinθ = cosθ = 1/√2.
3. Calculate sin⁴θ + cos⁴θ:
sin⁴θ + cos⁴θ = (sin²θ)² + (cos²θ)²
= (1/2)² + (1/2)²
= 1/4 + 1/4
= 1/2.
The question is based on Chapter 8 of the Class 10th NCERT Mathematics textbook, titled “Introduction to Trigonometry.” Provide your response in line with the concepts covered in this chapter.
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