Question

if sin A+sin²A=1, find cos²A+cos⁴A​

Answer 1

${ \underline{ \red{ \bold{Given}}}}$

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

${ \underline{ \green{ \bold{Find}}}}$

${ \sf{➢ {cos}^{2}A+ {cos}^{4}A}}$

${ \underline{ \blue{ \bold{Solution}}}}$

${ \sf{⟶sin \: A+ {sin}^{2} A = 1}}$

${ \sf{⟶ {sin}^{2} \: A = 1 - sin \: A......(1) }}$

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

From trigonometry identity...,

${ \boxed{ {sin}^{2} a + {cos}^{2}a = 1 }}$

${ \boxed{ \therefore{ {cos}^{2} \: a = 1 - {sin}^{2} a}}}$

${ \sf{⟶ {cos}^{2} a + {cos}^{4} a = 1 - {sin}^{2} a + { {(cos}^{2} a)}^{2} }}$

${ \sf{⟶1 - {sin}^{2} a + { {(1 -sin}^{2} a)}^{2} }}$

${ \sf{⟶1 - {sin}^{2} a + {(1 - (1 - sin \: a))}^{2} }}$

${ \sf{⟶1 - {sin}^{2} a + {sin}^{2} a}}$

${ \sf{⟶ {cos}^{2} a + {sin}^{2} a = 1}}$

Therefore,Cos²A+cos⁴A=1

Trigonometry identities:-

${ \boxed{ {sin}^{2} a + {cos}^{2} a = 1}}$

${ \boxed{ {tan}^{2} a = 1 - {sec}^{2} a}}$

${ \boxed{ {cot}^{2} a = 1 - {cosec}^{2} a}}$

Answer 2

Answer:

1

Step-by-step explanation:

SinA + Sin²A=1

or, SinA = 1-Sin²A

or, SinA = Cos²A

Cos²A+Cos⁴A

= Cos²A + (Cos²A) ²

= Sin A + Sin²A

= 1

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