Question

If sin teta + sin^2teta = 1 then cos^2teta+ cos ^4teta
(1) 1
(2) 2
(3) 3
(4) V2​

Answer 1

$\displaystyle\textcolor{red}{SOLUTION}$

GIVEN

$sinθ \: + {sin}^{2} θ \: = 1$

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

$\implies \: sinθ \: = {cos}^{2} θ \:$

HENCE

${cos}^{2} θ \: + {cos}^{4} θ \:$

$= {cos}^{2} θ \: + { ({cos}^{2}θ) }^{2}$

$= {cos}^{2} θ \: + { sin}^{2} θ$

$= 1$

Hence the required answer is 1

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