Rút gọn: $a)A=cos(90-x).cos(180-x)$ $b)B=cos(90-x).cot(180-x)$ $c)C=cos(90-x)-sin(180-x)$

Đáp án+Giải thích các bước giải:

 `a)`

`A=cos(90^{o}-x).cos(180^{o}-x)`

`=sinx. (-cosx)`

`=-sin x cos x`

Vậy `A=-sin x cos x`

`b)`

`B= cos(90^{o}-x). cot(180^{o}-x)`

`=sinx . (-cot x)`

`=-sin x .cot x`

`=-sin x. \frac{cos x}{sin x}`

`=-cos x`

Vậy `B=-  cos x`

`c)`

`C=cos(90^{o}-x)-sin(180^{o}-x)`

`=sin x- sin x`

`=0`

Vậy `C=0`

____________________________

Ta áp dụng:

$\bullet$ `sin(90^{o}-x)=cos x`

$\bullet$ `cos(90^{o}-x)= sin x`

$\bullet$ `tan(90^{o}-x)=cot x`

$\bullet$ `cot(90^{o}-x)=tan x`

$\bullet$ ________ $\bullet$ _______ $\bullet$ _________ $\bullet$

$\bullet$ `sin(180^{o}-x)=sin x`

$\bullet$ `cos(180^{o}-x)=-cos x`

$\bullet$ `tan(180^{o}-x)=-tan x`

$\bullet$ `cot(180^{o}-x)=-cot x`