Question

if A=cos2theta+ sin4theta for all value of theta , where A belongs [a,b] , then 4a+b is​

Answer 1

⭐Required answer:-

A=cos 2 θ+sin 4θ

A=cos 2 θ+sin 2 θsin 2 θ≤cos 2 θ+sin 2 θ

A=cos 2 θ+sin 2 θsin 2 θ≤1 (sin 2 θ+cos 2 θ=1). ----(1)

or A=cos 2θ+sin 4 θ

A=(1−sin 2 θ)+sin 4 θ

A=(sin 2 θ) 2 +( 21 )

2 −2× 21 ×sin 2θ+(1− 41 )

A=(sin 2 θ− 21 ) 2 + 43 ≥ 43

----------(2)

From equation 1 and 2,

43 ≤A≤1

so option B will be the correct answer