2. b) 2+(cos *) 2] 2-2 [sin * cos *] 2 = 5/9 is derived from the original formula, so sin2 * = 2sin * cos * = b.

3. B. First decompose the factor to get sin*=24/25 or-1 (discarded), so cos*=-7/25, and then use the double angle formula to get the answer as A or B. And sin*=24/25, so the answer is B.

4.c

5. Root number 2. Use cos 100=-sin 10 and the double angle formula. Sin100 = 2sin50cos 501= sum of squares of sin50 and cos50.

9.y=2(cosx)^2+2(cosx/2)^2

=2(cosx)^2+cosx+ 1

=2(cosx+ 1/4)^2+7/8

Since cosx is greater than or equal to-1 and less than or equal to 1, and from tanx/2 and tanx, it is known that cosx is not equal to positive and negative root signs 1/2 and 0, y is greater than or equal to 7/8 and less than or equal to 4, and y is not equal to 1 and 2+ root signs 65438 and 2- root signs 65438.

10. First, explain & stands for 180 degrees, and let m = sin (x+&; /4)。

y=sinxcosx+a(sinx+cosx)+a^2

=sin2x/2+ radical number 2× asin (x+&; /4)+a^2

=- 1/2cos(2x+& amp； /2)+ radical sign 2× asin (x+&; /4)+a^2

= sin(x+& amp； /4)2+ radical 2× asin (x+&; /4)+a^2- 1/2

=(m+a/ radical number 2) 2+ 1/2a 2- 1/2

Therefore, when a takes root number 2 and m takes 1, y is the largest, which is 9/2. And there is no minimum.