Question

solve it with explanation​

Answer 1

Given:-

• $\rm\sin A + \sin^2 A = 1$

To Prove:+

• $\rm\cos^2A+\cos^4A = 1$

$\rule{320}{1}$

• We will use only one identity:-

• $\rm 1-\sin^2\theta = \cos^2\theta$

Proof:-

$\rm\textsf{Consider }\sin A + \sin^2A=1 \\\\\\ \implies \rm \sin A=1-\sin^2A\\\\\\ \implies \rm\sin A=\cos^2A \\\\\\ \textsf{Squaring both sides} \\\\\\ \implies\rm \sin^2 A=\cos^4 A \\\\\\ \implies \rm 1-\cos^2 = \cos^4A\\\\\\ \implies \rm 1 = \cos^2 A+\cos^4 A \\\\\\ \implies \boxed{\rm \cos^2A+\cos^4A=1} \\\\\\ \mathcal{HENCE\ \ PROVED}$

Answer 2

sin A + sin² A=1

sin A=1-sin²A

(sin)²=(cos²A)²

sin²A=cos⁴A

1-cos²A=cos⁴A

cos²A+cos⁴A=1

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