Find the value of (cos(x) + sec(x))^2 with respect to x when evauated between pi/4 and 0

first we have to see if this proble can be done via inspection. The power of two means that this can't be done straight away and the expression does not look like any trig identities.
Expand it.
through this simple expansion, the sec .cos term becomes unity and the cos^2 term and sec^2 are left.the sec^2 term can be integrated to tanx and the cos^2 aftter rearranging in terms of cos(2x) can also be integrated. After subbing in the limits, the answer becomes (5/8) *(2 + pi)