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Someone show me step for step please!

Someone show me step for step please!-example-1
User Amal Ps
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2 Answers

7 votes


\csc \theta \tan \theta - \tan \theta \sin \theta \\\\\\=\frac 1{\sin \theta} \cdot (\sin \theta )/(\cos \theta )- (\sin \theta )/(\cos \theta) \cdot \sin \theta\\\\\\=(1)/(\cos \theta)-(\sin^2 \theta)/(\cos \theta)\\\\\\=(1- \sin^2 \theta)/(\cos \theta)\\\\\\=(\cos^2 \theta)/(\cos \theta)~~~~~~~~~~~~~~;[\sin^2 \theta + \cos^2 \theta =1 ]\\\\\\=\cos \theta

User Owenwater
by
8.3k points
1 vote

Let's write out some trigonometric identities that we can use:


  • tan(x)=(sin(x))/(cos(x)) \\

  • csc(x)=(1)/(sin(x))

  • sin^2(x)+cos^2(x)=1
    cos^2(x)=1-sin^2(x)

Now let's try solving them out:


csc(x)tan(x)-tan(x)sin(x)=(1)/(sin(x))tan(x)-sin(x)tan(x)\\\\ csc(x)tan(x)-tan(x)sin(x)=tan(x)((1)/(sin(x))-sin(x))\\\\ csc(x)tan(x)-tan(x)sin(x)=tan(x)((1)/(sin(x)) -(sin^2(x))/(sin(x)) )\\\\csc(x)tan(x)-tan(x)sin(x)=tan(x)*((1-sin^2(x))/(sin(x)) )\\\\csc(x)tan(x)-tan(x)sin(x)=(sin(x))/(cos(x))*(cos^2(x))/(sin(x)) \\\\csc(x)tan(x)-tan(x)sin(x)=(sin(x))/(sin(x))*(cos^2(x))/(cos(x))\\\\csc(x)tan(x)-tan(x)sin(x)=1 * cos(x)\\\\ csc(x)tan(x)-tan(x)sin(x)=cos(x)

*I used a different variable, but that doesn't change the answer

Answer: cos(x)

Hope that helps!

User Llighterr
by
7.7k points

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