(sin(x)+tan(x))/(cos(x)+1)=tan(x)

How can you verify this identity? With lots of clear steps please :)

(sin(x)+tan(x))/(cos(x)+1)=tan(x)

change tan(x) to sin(x) over cos(x)

(sin(x)+sin(x)/cos(x))/(cos(x)+1)

find a common denominator

(sin(x)cos(x)/cos(x)+sin(x)/cos(x))/(c…

((sin(x)+sin(x)cos(x))/cos(x))/(cos(x)…

factor our sin(x) in the numerator

((sin(x)(1+cos(x)))/cos(x))/(1+cos(x))

divide the fraction in the numerator and the fraction in the denominator

(sin(x)(1+cos(x))/cos(x) / 1+cos(x)/1

remember dividing fraction means to multiply by the reciprocal (flip the second fraction) and multiply across

(sin(x)(1+cos(x))/cos(x)) x 1/(1=cos(x))

so the (1+cos(x)) will cancel and you get

sin(x)/ cos(x)

which is

tan(x)

Hope this helps

Nicole -

Here are the "clear" steps. For simplicity, I'll ignore the x's

(sin + tan)/(cos +1)

(sin + sin/cos) / (cos + 1) , now factor out sin

sin(1 + 1/cos) / (cos + 1), now get common denominator of cos

[sin(cos + 1)/cos ] / (cos + 1) , next (cos +1) cancels out

sin/cos = tan

Hope that helped