Trigonometric Equations: solve 1 + sinx + 2cosSQ(x)

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Solve each equation below on the interval 0 less than or = to theta less than 2 pi.

I will use SQ to represent the word squared.

1) 1 + sinx = 2cosSQ(x)

Should I convert 2cosSQ(x) to 1 - 2sinSQ(x) and equate BOTH sides?

If so, how do I factor afterward?

2) 3 - sinx = cos2x

For question 2, I got: pi/2, 0, 2pi and pi as my asnwers but the textbook tells me that I am wrong.

If so, how do I solve question 2? What are the steps? If I need to factor, can someone please show me how to factor trig equations?
 
1) Converting 2cos<sup>2</sup>(x) to 2(1 - sin<sup>2</sup>(x)) would be a good way to start. Then move everything over to the left-hand side, simplify, and solve the resulting quadratic for "sin(x)=". (You can use the Quadratic Formula, if you like.) Then solve the resulting trig equations.

2) How did you get your answers?

I would convert the cos(2x) to a 1 - sin<sup>2</sup>(x), and then follow the same technique as for (1) above.

Eliz.
 
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