Question

15. If sin - cos = 0,
then find the value of
(sin^4+ cos^4).​

Answer 1

Step-by-step explanation:

Given :-

sin- cos = 0

To find :-

sin⁴ + cos⁴

squaring both side

(sin - cos)² = (0)²

sin² + cos² - 2sincos = 0

sin² + cos² = 2sincos

squaring both side

(sin² + cos²)² = (2sincos)²

sin⁴ + cos⁴ + 2sin²×cos² = 4sin²×cos²

Since, sin²×cos² = 1

sin⁴ + cos⁴ + 2×1 = 4 × 1

sin⁴ + cos⁴ = 4 - 2

sin⁴ + cos⁴ = 2

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Answer 2

Answer:

sin-cos=o.

• squaring both sides (sin-cos)^2=o sin^2+cos^2-2sin.cos=0 sin^2+cos^2 = 2sin.cos