Question

How do you simplify the expression `cost/(1+sint)+cost/(1-sint)`?

Answer 1

`2sect`

Explanation:

Begin by expressing the sum of the 2 fractions as a single fraction. This requires having a common denominator.

`rArr(cost)/(1+sint)xx(1-sint)/(1-sint)+(cost)/(1-sint)xx(1+sint)/(1+sint)`

`=(cost(1-sint)+cost(1+sint))/((1+sint)(1-sint))`

distributing the brackets on numerator and denominator

`=(cost-costsint+cost+costsint)/(1-sin^2t)`

`color(orange)"Reminder " color(red)(|bar(ul(color(white)(a/a)color(black)(sin^2t+cos^2t=1rArr1-sin^2t=cos^2t)color(white)(a/a)|)))`

simplifying numerator/denominator gives.

`(2cost)/(cos^2t)=(2cancel(cost)^1)/(cancel(cost)^1cost)=2/cost=2sect`

`color(orange)"Reminder " color(red)(|bar(ul(color(white)(a/a)color(black)(sect=1/cost)color(white)(a/a)|)))`

`rArr(cost)/(1+sint)+(cost)/(1-sint)=2sect`