Question

If sin^2 0 + sin 0 = 1, then prove that cos^2 0 + cos^4 0 = 1

Answer 1

Answer:

$\implies {sin}^{ \: 2} \: \theta + sin \: \theta \: = 1$

$\implies \: sin \: \theta \: = 1 - {sin}^{2} \: \theta$

We know that,

1- sin^2 = cos ^2

$\implies \: sin \: \theta \: = {cos}^{ \: 2} \: \theta \: .........eq \: 1$

Now, substitute ,

$\therefore \: {cos}^{2} \: \theta \: + {cos \: }^{4} \: \theta = sin \: \theta \: + \: {sin}^{2} \: \theta = 1$

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hope it helps.....

Answer 2

Step-by-step explanation:

sin²o +sin o = 1

1= sin²o +cos²o ---A

sin²o + sin o = sin²o + cos²o

removing sin²o on both sides

sino = cos²o

squaring on both sides

sin²o = cos⁴o ----B

substitute B in A

cos²o+ cos⁴o=1