Prove that sin x + cos x the whole square is equal to 1 + sin 2x

In the given figure ar(adf) =ar(cda) and ar(cdf) = ar(cdf). show that abdc and cdfe are trapeziums.

Each month, a shopkeeper spends 5x + 14 dollars on rent and electricity. if he spends 3x−5 dollars on rent, how much does he spend on electricity? for which value(s) of x is the amount the shopkeeper spends on electricity less than $100? explain how you found the value(s).

What is the measure of angle tvu shown in the diagram below