If sinx + sin²x = 1, then find the value of cos²x + cos⁴x.
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Correct answer: C
Explanation
Has been given :
sinx + sin²x = 1
According to the formula:
sin²x + cos²x = 1
sin²x = 1 − sinx
Now
cos²x = 1 − sin²x
= 1 − (1 − sinx)
= sinx
cos⁴x = (cos²x)²
= (sinx)²
= sin²x
cos²x + cos⁴x
= sinx + sin²x
= 1