Question

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

Answer 1

Explanation:

1) 6 tan2x − 6 tan2x sin2x

=
`6tan2x(1-sin2x)\\= 6tan2x (sin^2 x + cos^2 x -2sinx cosx)\\= 6tan2x (sinx+cosx)^2\\`

2)
`(3)/(1+cos x) +(3)/(1-cosx) \\=(3-cosx+3+cosx)/(1-cos^2 x) \\=(6)/(sin^2 x) \\=6 cosec^2 x`

3)
`(sin^2 y)/(1-cosy ) =(1-cos^2 y)/(1-cosy )\\=1+cosy`

4) x=6cos t

So cost =x/6

`sint = \frac{√(36-x^2) }{\{6 } \\`

so -3sint

5)