Question

if sin theta + sin^2 theta = 1 , prove that cos ^2 theta + cos^4 theta = 1

Answer 1

Answer:

In the attachment.. Hope it's helpful.?

Answer 2

$\huge{ \underline{ \bold{ \blue{solution}}}}..........$



$\sin \theta \: + {sin}^{2} \theta \: = 1 \: \: \: \: \: \huge{eq(a.)}\: \: \: \: \: \: \: \green{it \: is \: given \: in \: the \: question}$
$sin \theta \: = 1 - {sin}^{2} \theta \\ \\ sin \theta \: = {cos}^{2} \theta \: \: \: .......... eq(1.)$


NOW,



$\huge{ \underline{ \bold{ \red{left \: hand \: side}}}}$


$= {cos}^{2} \theta \: + {cos}^{4} \theta \:$
$\huge{from \: eq.(1.)}$


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


$= 1 = \huge{ \underline{ \bold{ \red{ \: right \: hand \: side}}}}$


Therefore RHS = LHS



$\huge{ \underline{ \bold{ \pink{ \: hence \: proved}}}}$