Question

If sin +sin^2 = 1 show that cos^2 +cos^4 =1​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

we have shown that

${cos}^{2}x + {cos} ^{4} x =1$

Step-by-step explanation:

we have

$sin x+ {sin}^{2} x= 1 \: \: \: \: \: \: \: \: \: \: (1)$

and we need to show

${cos}^{2}x + {cos} ^{4} x = 1 \: \: \: \: \: \: \ \: \: \: (2)$

we have from equation (1)

$sinx = 1 - {sin}^{2}x\: \: \: \: \: \: \: \: \: \: \: \: (3)$

we know

${cos}^{2}x = 1 - {sin}^{2}x$

consider equation (2)

${cos}^{2}x + {cos} ^{4} x =(1 - {sin}^{2}x) + ({cos}^{2}x)^{2}$

${cos}^{2}x + {cos} ^{4} x =(1 - {sin}^{2}x )+ (1 - {sin}^{2}x)^{2}$

now put equation (3) and we get

${cos}^{2}x + {cos} ^{4} x =sinx + (six)^{2}$

now from equation (1) we can write

${cos}^{2}x + {cos} ^{4} x =1$