Question

If cos A + cos² A = 1, prove that sin² A+ sin⁴A = 1​

Answer 1

Answer:

$\sf cos \: A+ cos² A=1$

$\sf \: cos \: A=1-cos² A$

$\sf \: cos \: A = sin² A$

$\sf \:LHS = sin² A+ {sin}^{4} A$

$\implies \sf sin² A+ (sin² \:A )$

$\sf \implies \:sin² A+ (cos A) ²$

$\sf \implies \: sin² A+ cos \: A$

$\sf \implies \: 1$

Hence proved

Answer 2

Answer:

${ \large{ \pmb{ \sf{★Given.. .}}}}$

CosA + Cos²A = 1

${ \large{ \pmb{ \sf{★Used \: Identity... }}}}$

Sin²A + Cos²A = 1

${ \large{ \pmb{ \sf{★ To \: Prove... }}}}$

sin² A+ sin⁴A = 1

${ \large{ \pmb{ \sf{★Solution... }}}}$

From, CosA + Cos²A = 1

${ \implies{ \sf{CosA + Cos²A = 1}}}$

$\: { \implies{ \sf{CosA = 1 - Cos²A}}}$

$\: { \implies{ \bold{ CosA = Sin²A...(1)}}}$

So, From this CosA is equal to two SinA's

${ \implies{ \sf{Sin⁴A + Sin²A = 1}}}$

Substitute equation (1) ,

${ \implies{ \sf{Cos²A + CosA = 1}}}$

${ \mathbb{ \blue{HENCE \: \: \: PROVED...!! }}}$