1.   = 1  ====>   = 0  =====>

    solve this quadratic equation for sin(x) to get a single value for sin(x) = .


2.   = 1  ====>  sin(x) =  = .

    Thus  = .


3.   =  =  = 

    =  .  =  = 1.


4.  ====>   = 1 - 2 = -1.

Subtracting sin2(x) from both sides,



Using a well-known Pythagorean identity,



Switching sides,



So, for that equation,
raising both sides to the 6th power gives 
raising both sides to the 5th power gives 
raising both sides to the 4th power gives 
raising both sides to the 3rd power gives 

So this



upon substituting those, becomes



Factoring out sin3(x) out of the first 4 terms,



Using the fact that (A+B)3 = A3+3A2B+3AB2+B3,



Writing the product of cubes as the cube of the product,



Distributing,



Reversing the terms,



Notice that what's in the parentheses is exactly what is 
given as equal to 1 in the beginning, so







Edwin

Since it's multiple choice and you don't have to understand 
anything at all as long as you get the right answer, the easy 
way is to just use your TI-83 or TI-84.  Mindlessly, follow 
this recipe:

Press Y=

Make screen read:

\Y1=sin(X)+sin(X)2
\Y2=1


Press ZOOM
Press 7
Press 2ND
Press TRACE
Press 5
Press ENTER
Press ENTER
Press ENTER
Press 2ND
Press MODE
Press CLEAR

Make the main screen read

cos(X)^12+3cos(X)^10+3cos(x)^8+cos(x)^6-2

Press ENTER

See  -1   

Edwin