Why can $cos^4 θ$ be written as $(cos^2 θ)^2$ ?

Question

Why can the θ have a square after that?

2149 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-18T09:48:35

As proved below.

As per theory of indices,

$a^m * a^n = a^(m+n)$

$(a^m)^n = a^(mn)$

$cos^4 theta = cos^(2 + 2) theta$

$=> cos^2 theta * cos^2 theta = (cos^2 theta)^2$

Answer 2 · 2018-06-19T02:22:47

$cos^2 theta$ is shorthand for $(cos theta)^2$ and $cos^4 theta$ is shorthand for $(cos theta)^4.$ So,

$cos^4 theta = (cos theta)^4 = ( (cos theta)^2) ^2 = (cos^2 theta)^2$