Question

Reduce the given trigonometric expression to a number:

sin(x)+3tan(x)cot(x)-1/csc(x) -sec^2(x)+tan^2(x)

the 1/csc(x) is a fraction so the 1 is the numerator and csc(x) is the denominator

Answer 1

`\bf 1+tan^2(\theta)=sec^2(\theta)\implies 1=sec^2(\theta)-tan^2(\theta)\\\\ \cfrac{1}{csc(\theta)}=sin(\theta)\qquad \qquad cot(\theta)=\cfrac{1}{tan(\theta)} \\\\`