Question 1

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

Question 2

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

$\bf -----------------------------\\\\ \begin{array}{cccccccccc} sin(x)&+&3tan(x)cot(x)&-&\cfrac{1}{csc(x)}&-&sec^2(x)+tan^2(x)\\ \downarrow &&\downarrow &&\downarrow &&\downarrow\\ &&3tan(x)\cfrac{1}{tan(x)}&&sin(x)&&-[sec^2(x)-tan^2(x)]\\\\ sin(x) &+&3&-&sin(x) &-&1 \end{array}\\\\ -----------------------------\\\\ sin(x)+3-sin(x)-1\implies 3-1\implies\boxed{ 2}$

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