Write 'True' or 'False' and justify your answer. If cos A+cos ^{2} A=1, then sin ^{2

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8. Introduction to Trigonometry

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Write 'True' or 'False' and justify your answer.

If $\cos A+\cos ^{2} A=1,$ then $\sin ^{2} A+\sin ^{4} A=1$

Option A

Option B

Option C

Option D

Solution

True.

$\because \cos A+\cos ^{2} A=1$

$\cos A=1-\cos ^{2} A=\sin ^{2} A \quad\left[\because \sin ^{2} A+\cos ^{2} A=1\right]$

$\cos ^{2} A=\sin ^{4} A$

$1-\sin ^{2} A=\sin ^{4} A$

$\sin ^{2} A+\sin ^{4} A=1 \quad\left[\because \cos ^{2} A=1-\sin ^{2} A\right]$

Standard 10

Mathematics

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