1 to understand the meaning of the question, AD=(4 root number 15)/3, AC=2 root number 5, so cos∠CAD= (root number 3)/2, so ∠CAD=30 degrees, so ∠A=60 degrees, and.

2 solution 1 because this is a multiple-choice question, we adopt the special value method according to the conditions and the principle of multiple-choice questions. Now, according to the meaning of the topic, we choose ∠A=60 degrees, which obviously meets the setting conditions of the topic. From this, we can calculate sinA= (root number 3)/2, cosA= 1/2 and tanA= root number 3, so that we can know Tana & sinA & gtCosA. Option d

Scheme 2: Graphic method, first draw the image of Sina in cosA at [0, pi/2]. According to the meaning of the question, a belongs to [45 degrees, 90 degrees], so it can be clearly seen on the way that Sina is bigger than cosA, and Tana's image is drawn in the same way, which shows that Tana is bigger than Sina, thus reaching the same conclusion D.

Solving the three-coordinate method, we know that in the coordinate system, cosA and sinA are the ratios of the lengths of X, Y and X+Y in a right triangle composed of vectors X, Y and X+Y respectively. Because of 45 degrees

To solve inequality 4, shilling X=sinA-cosA, then x = tana * COSA-COSA = COSA (tana-1), 45 degrees.

Note: In the actual problem-solving process, it is recommended to use the method 1 because it is the fastest and most time-saving. However, methods 2 and 3 should also be clarified, because method 1 is only a skill of selection, and the real knowledge lies in methods 2, 3 and 4.