Question

2) If sin A + sin² A = 1, then the value of cos²A + cos 4A is​

Answer 1

Step-by-step explanation:

Given

sina+sin2a=1

⇒sina=1−sin2a

⇒sina=cos2a

⇒sin2a=cos4a

⇒1−cos2a=cos4a

⇒cos2a+cos4a=1

Answer 2

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

$\sin a = 1 - { \sin}^{2} a$

$using \: identity \\ { \sin}^{2}a + { \cos}^{2}a = 1$

$\sin a = { \cos }^{2}a$

$squaring \: both \: sides$

${ \sin }^{2} a = { \cos }^{4} a$

Now,

${ \cos }^{2}a + \cos4a$

as cos⁴a = sin² a

so,

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

Hence, Cos²a + Cos⁴a = 1