a. B is a non negative number √ (1-A ^ 2) √ (1-B ^ 2) = ab

In addition to the "trigonometric substitution method" on the first floor, it can also be proved directly by algebraic method: because a and B are non negative real numbers, the root sign (1-A ^ 2) * root sign (1-B ^ 2) = AB = = > (square of both sides, sorting) a ^ 2 + B ^ 2 = 1; therefore, a root sign (1-B ^ 2) + B root sign (1-A ^ 2) = a root sign a ^ 2 + B root sign b ^ 2 = a ^ 2 + B ^ 2 = 1

RELATED INFORMATIONS

1. If a > b > C, a + 2B + 3C = 0, AB > AC and ab
2. In space quadrilateral ABCD, ab ⊥ CD, BC ⊥ Da, prove: ab ^ 2 + CD ^ 2 = BC ^ 2 + Da ^ 2
3. If two points c and D outside the line BC are known, CA = CB, Da = dB, and the straight line CD intersects AB at O, then point O is the midpoint of AB, and CD is the vertical bisector of ab
4. It is known that C and D are points outside the line AB, and Ca = CB, Da = dB. It is proved that the straight line CD bisects AB vertically Prove with the vertical bisector of line segment
5. If we know the line AB and the points c, D, and Ca = CB, Da = dB, then the line CD is the integral of the line ab______ ．
6. C. D is the point outside the line AB, and Ca = CB, Da = ab Please use the theorem of vertical bisector. No auxiliary line is allowed
7. As shown in the figure, D is a point in the quadrilateral aebc, connecting AD and BD. it is known that Ca = CB, Da = dB and EA = EB. (1) are the three points c, D and E in a straight line? Why? (2) If AB = 24, ad = 13, CA = 20, what is the length of CD?
8. As shown in the figure, (1) (2) Ca = CB, Da = dB, prove that CD is the vertical bisector of ab
9. It is known that, as shown in the figure, CA = CB
10. As shown in the figure, CA = CB, Da = dB
11. It is proved that if a, B ∈ R, then at least one of a ^ 2 + AB and B ^ 2 + AB is non negative Good answer points
12. Known: 0 〈 a 〈 1, proof: 1 / a 4 / (1-A) greater than or equal to 9
13. Try to prove the inequality by analysis: (1 + 1 / sin ^ a) (1 + 1 / cos ^ a) > = 9
14. The proof of inequality in the second year of senior high school This is a thinking problem in my homework It is known that a > b > 0 (a-b)^2/8a
15. Analysis and synthesis to prove inequality If positive numbers a and B satisfy AB = a + B + 3, then the value range of AB is?
16. Senior high school mathematical inequality proof: when a > 0, b > 0, 1 / AB + 1 / a (a-b) > = 4 / A ^ 2
17. A + B = - 2 find the maximum value of ab Using inequality
18. Let f (x) = x2 + BX + 1, and f (- 1) = f (3), then the solution set of F (x) > 0 is () A. （-∞，-1）∪（3，+∞）B. RC. {x∈R|x≠1}D. {x∈R|x=1}
19. When a is a value, the solution of the equation a (3x-1) = 4x + 7 is positive, and when a is a value, the solution of the equation is in the interval [- 3,2]?
20. A & # 178; + B & # 178; + ab ≥ 0