Đáp án`+`Giải thích các bước giải:

`1.(B)`

`A= tan^2 alpha + cot^2 alpha`

`= (tan^2 alpha -2tan alpha . cot alpha + cot^2 alpha)+2 tan alpha . cot alpha`

`= (tan alpha - cot alpha)^2 +2`

`= 3^2 +2=11`

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`2.(D)`

`A= tan 1^@ .tan 2^@ ...tan 89^@`

`= (tan 1^@ . tan 89^@ ).(tan 2^@ .tan 88^@ )...(tan 44^@ .tan 46^@). tan 45^@`

`= (tan 1^@ . cot 1^@ ).(tan 2^@ .cot 2^@ )...(tan 44^@ .cot 44^@). 1`

`=1`

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`3.(C)`

`sin^2 2^@ + sin^2 4^@ +...+sin^2 88^@`

`= (sin^2 2^@ + sin^2 88^@ )+(sin^2 4^@ + sin^2 86^@ )+...+ (sin^2 44^@ + sin^2 46^@ )`

(có `22` nhóm)

`=( sin^2 2^@ + cos^2 2^@ )+( sin^2 4^@ + cos^2 4^@ )+...+( sin^2 44^@ + cos^2 44^@ )`

`=1+1+...+1 =22`

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`4.(B)`

Xét: `sin^2 alpha + cos^2 alpha=1`

`=> ( sin^2 alpha +2sin alpha . cos alpha  + cos^2 alpha )-2sin alpha . cos alpha =1`

`=> (sin alpha + cos alpha )^2 - 2.sin alpha . cos alpha =1`

`=> (sqrt(2))^2 - 2.sin alpha . cos alpha =1`

`<=> sin alpha . cos alpha = 1/2`

Xét: `sin^4 alpha + cos^4 alpha`

`= (sin^2 alpha + 2.sin^2 alpha . cos^2 alpha + cos^4 alpha ) -  2.sin^2 alpha . cos^2 alpha `

`= (sin^2 alpha + cos^2 alpha ) - 2. (1/2)^2`

`= 1- 1/2 = 1/2`

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`5.(A)`

Chọn `x` mang giá trị bất kì, chạy `x= 1^@`

`-> f(x)= 1`

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`6.(A)`

Chọn `x` mang giá trị bất kì, chạy `x= 1^@`

`->` giá trị biểu thức `=1`

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`7.(B)`

Chọn `x` mang giá trị bất kì, chạy `x= 1^@`

`->` giá trị biểu thức `=0`

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`8.(B)`

`A= tan 5^@ .tan 10^@ ...tan 85^@`

`= (tan 5^@ . tan 85^@ ).(tan 10^@ .tan 80^@ )...(tan 40^@ .tan 50^@). tan 45^@`

`= (tan 5^@ . cot 5^@ ).(tan 10^@ .cot 10^@ )...(tan 40^@ .cot 40^@). 1`

`=1`

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`9.(B)`

Bấm máy ta được giá trị: `B=2`

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`10.(D)`

`tan^2 alpha + cot^2 alpha =7`

`=> (tan^2 alpha + 2. tan alpha . cot alpha + cot^2 alpha )- 2. tan alpha . cot alpha =7`

`<=> (tan alpha + cot alpha )^2 - 2=7`

`=> m^2 =9`

`<=> m=+-3`