Question

if sin^ 2 a + sin ^4 a =1 , then prove that cos ^2 a + cos a =1

Answer 1

$\mathfrak{\huge{\green{\underline{\underline{Answer :}}}}}$

cos A+cos^2 A=1 ————(1)

cos A =1-cos^2 A

[sin^2 A=1- cos^2 A]

cos A= sin^2 A ———-(2)

Substitute value of cos A in Eqn. (1)

(sin^2 A) + (sin^2 A)^2=1

sin^2 A + sin^4 A=1 [Proved]

Answer 2

sin^2a + sin^4a =1

sin^2a=1-(sin^4a)

sin^2a=(1-sin^2a)^2

sin^2a=(cos^2)^2 ........(1-sin^2a=cos^2a)

sin^2a=cos^4a

1-cos^2a=cos^4 ........(sin^2a=1-cos^2a)

1=cos^4a-cos^2a