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1 cosa is equal to 1 1 5 square open root number is equal to 2 5 times root number 6 tana is equal to sina divided by cosa is equal to 1 12 times root number 6 cota is equal to 2 times root number 6

2 cota is equal to 1 divided by 8 out of 15 equals 15 out of 8 sina cosa tana

cosa is equal to the square of 1 sina under the root number.

Synoptic can solve sina equal to 8/17 and COSA equal to 15/17

sina = y r = 1 5, so x = plus and minus root sign under r 2-x 2 = plus and minus root number 24

So cosa=xr=plus/minus root number 24 5

tana = y x = plus or minus 1 root number 24 = plus or minus root number 24 24 first quadrant positive, second quadrant negative).

tana=y x=8 15, so r=x 2+y 2=225+64=17 under the root

So sina = y r = plus or minus 8 17

cosa = plus or minus 15 17

The first quadrant is positive, the third quadrant is negative).

There is no simplification. I guess there should be a positive and negative score

Answer: 1 sina 2+cosa 2=1, and a is an acute angle, so the cosine function of cosa=sqr( is the quadratic arithmetic root of 1 minus the square of the sine function, because a is an acute angle. ）

tga=sina/cosa=

ctga=2 tga=, ctga=1/tga=

tga=sina cosa=8 15, so let sina = 8x, cosa = 15x, in the consist of 64x 2 + 225x 2 = 1

The solution is: x1=sqr(1 289), x2=-sqr(1 289) is deleted (because a is an acute angle).

So sina = , cosa =

x1+x2=a

x1x2=a-2

x1-x2)^2=(x1+x2)^2-4x1x2=a^2-4(a-2)=a^2-4a+8=(a-2)^2+4

When a=2, the absolute value of x1-x2 is the minimum value, (x1-x2) 2=(a-2) 2+4=4

The minimum value is 2

a=2 The minimum value is 2

ix1-x2i=open root(x1-x2)= open root (x1+x2)squared-4x1x2=......

Do you understand? Will you do it later? Because it's too troublesome to square the roots. If you don't, ask again.

According to the root finding formula, x1 = 2 x2 = = 2

Let the absolute value of the difference between the two roots = y

y=|x1-x2|=|sqrt[a^2-4(a-2)]|It can be seen that miny=min[a 2-4(a-2)] let f(a) = a 2-4(a-2).

The formula shows that f(a)=(a-2) 2+4 that is, when a=2, the minimum value is obtained and a=2 is brought in, and the minimum value is miny=2

Note: sqrt open square root, min min).