Can someone help solve these math problems

Simplify the trigonometric expression.
sin^3(x)+cos^2(x)sin(x)

Simplify the trigonometric expression.
1+cot(x)/csc(x)

first person to give me both correct answers will get best answer.

first one, factor out the sin(x)... sin(x)*[sin^2(x) + cos^2(x)] the inside is the trig identity which equals 1.
so the answer is just sin(x)

second one can be re written as [ 1 + cos(x)/sin(x) ] / 1/sin(x) ... then you have sin(x) + cos(x).. based on the trig identity that sin^2(x) + cos^2(x) = 1 we conclude the answer is square root of 1.. which is just 1

Formula you should know:
1. sin²(x) + cos²(x) = 1
2. cot(x) = 1 / tg(x)
3. tg(x) = sin(x) / cos(x)
4. csc(x) = 1 / sin(x)

1. sin^3(x) + cos²(x) sin(x)
= sin(x) { sin²(x) + cos²(x) }... Using formula 1
= sin(x) { 1 }
= sin(x)

2. 1 + cot(x) / csc(x)
= 1 + { 1 / tg(x) } / { 1 / sin(x) }... Using formula 3 & 4
= 1 + { cos(x) / sin(x) } . sin(x)
= 1 + cos(x)

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