Question

if sin A+sin²A=1 then the value of cos²A+cis⁴A is​

Answer 1

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GiveN :

$\rightsquigarrow \sf \: \sin A + { \sin}^{2} A = 1$

To FinD :

$\rightsquigarrow \sf \: { \cos}^{2} A + { \cos}^{4} A = {?}^{}$

SolutioN :

~EXPRESSION :

$\: \: \: \: \: \: \: \: \: \: \: \sf \: \sin A + { \sin}^{2} A = 1$

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

$\implies \sf \: \sin A = { \cos}^{2} A$

$\circ \: \sf \: Now \: \: substituting \: \: the \: \: value \: \: of \: \: cos² \: A \: \: \& \:\: cos^4 \: A$

$\: \: \dashrightarrow \sf \: { \cos}^{2} A + { \cos}^{4} A {}^{}$

$\sf \implies \sin \: A + { \sin}^{2} A$

$\: \: \: \: \: \therefore \: \: \underline{ \boxed{ \sf \: 1 \: }} \: \: \: \: \: \: \bf[Given]$

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