Question

plz solve this question fast ​

Answer 1

$sinx - cosx = 0 \\ sinx = cosx \\ sinx = sin(90 - x) \: ...cosx = sin(90 - x) \\ x = 90 - x \\ 2x = 90 \\ x = {45}^{o} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ...(i) \\ \\ \: \: \: \: {sin}^{4} x + {cos}^{4} x \\ = {sin}^{4} {45}^{o} + {cos}^{4} {45}^{o} \: \: \: \: \: \: \: \: \: \: \: ...(from \: i) \\ = { (\frac{1}{ \sqrt{2} } )}^{4} + {( \frac{1}{ \sqrt{2} } )}^{4} \\ = \frac{1}{4} + \frac{1}{4} = \frac{2}{4} \\ = \frac{1}{2}$

Hence, sin⁴x + cos⁴x = 1/2.

Answer 2

correct answer is "c,"

1/2

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