Question

2sin^2A +cos^4A =1+sin^4A​

Answer 1

$\huge{\underline{\underline{\red{♡Solution→}}}}$

$2 {sin}^{2} a + {cos}^{4} a = 1 + {sin}^{4} a$

$\bold{\huge{\underline{\underline{\rm{ LHS :}}}}}$

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

$= 2 {sin}^{2} a + ( { {cos}^{2} a)}^{2}$

We know that →

• ${cos}^{2} a = 1 - {sin}^{2} a$

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

$= 1 + {sin}^{4} a$

$\bold{\huge{\underline{\underline{\rm{ </strong><strong>RHS</strong><strong> </strong><strong>↑</strong><strong>}}}}}$

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