Question

If
$\sin \: theta + { \sin \: }^{2} theta \: = 1$
then
${ \cos \:}^{2} theta \: + { \cos }^{4} \: theta = 1$
​

Answer 1

$\boxed{\huge{\red{\mathfrak{Question}}}}$

_________________________

let theta be x

If ,

$\mathtt{sin\:x+{sin}^{2}\:x=1}$

Then prove that ,

$\mathtt{{cos}^{2}\:x + {cos}^{4}\:x} = 1$

_________________________

$\boxed{\huge{\red{\mathfrak{Answer}}}}$

_________________________

Given:

→ sin x + sin² x = 1

→ sin x = 1 - sin² x

→ sin x = cos² x

By Squaring both sides,

→ sin² x = cos⁴ x

But sin² x = 1 - cos² x,

→ 1 - cos² x = cos⁴ x --------------------- ( 1 )

To prove:

cos² x + cos⁴ x = 1

Taking LHS ,

Put equation ( 1 ) in this ,

→ cos² x + 1 - cos² x

→ 1

LHS = RHS

Hence proved .