Question

Find: sin 2x + cos 4x​

Answer 1

Answer:

y=sin2(x)+cos4(x)————(1)

=1−cos2(x)+cos4(x)

=1−cos2(x)(1−cos2(x))

=1−cos2(x)sin2(x)

=1−4cos2(x)sin2(x)4

=1−(2cos(x)sin(x))24

=1−sin2(2x)4————(2)

As −1≤sin(2x)≤1

⟹0≤sin2(2x)≤1

⟹0≤sin2(2x)4≤14

⟹0≥−sin2(2x)4≥−14

⟹1−14≤1−sin2(2x)4≤1

⟹34≤y≤1

So, range of sin2(x)+cos4(x) is [34, 1]