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1) Factor the expression and use the fundamental identities to simplify. There is more than one correct form of the answer.

6 tan2x − 6 tan2x sin2x

2) Perform the addition or subtraction and use the fundamental identities to simplify. There is more than one correct form of the answer.

3/1+cos x + 3/1-cos x

3) Rewrite the expression so that it is not in fractional form. There is more than one correct form of the answer.

(sin^2y)/1-cos y

4) Use the trigonometric substitution to write the algebraic equation as a trigonometric equation of θ, where

−3sqrt1a.gif3=sqrt1a.gif36 − x2 , x= 6 cos θ

−3sqrt1a.gif3= _____

Find sin θ and cos θ

Respuesta :

Answer:

Step-by-step explanation:

1) 6 tan2x − 6 tan2x sin2x

=[tex]6tan2x(1-sin2x)\\= 6tan2x (sin^2 x + cos^2 x -2sinx cosx)\\= 6tan2x (sinx+cosx)^2\\[/tex]

2) [tex]\frac{3}{1+cos x} +\frac{3}{1-cosx} \\=\frac{3-cosx+3+cosx}{1-cos^2 x} \\=\frac{6}{sin^2 x} \\=6 cosec^2 x[/tex]

3) [tex]\frac{sin^2 y}{1-cosy } =\frac{1-cos^2 y}{1-cosy }\\=1+cosy[/tex]

4) x=6cos t

So cost =x/6

[tex]sint = \frac{\sqrt{36-x^2} }{\{6 } \\[/tex]

so -3sint

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