[Toán 11] Lượng giác

L

lp_qt

1. $3\cos^2 2x+3\sin^2 x+\cos^2 x=0$

$\iff 3.\cos^2 2x+3.\dfrac{1-\cos 2x}{2}+\dfrac{1+\cos 2x}{2}=0$

$\iff 3.\cos^2 2x-\cos 2x+2=0$ (vô nghiệm)


2. $3\sin^4 x+5\cos^4 x-3=0$

$\iff 3.(\dfrac{1-\cos 2x}{2})^2+5(\dfrac{1+\cos 2x}{2})^2-3=0$

$\iff 3.(\dfrac{1-t}{2})^2+5(\dfrac{1+t}{2})^2-3=0 ; t=\cos 2x$

Đây là phương trình bậc hai ẩn $t$
 
L

lp_qt

3. $(2\sin x-\cos x)(1+\cos x)=\sin^2 x$

$\iff (2\sin x-\cos x)(1+\cos x)=1-\cos^2 x=(1+\cos x)(1-\cos x)$

TH1: $1+\cos x=0$

TH2: $2\sin x-\cos x=1-\cos x \iff \sin x=\dfrac{1}{2}$
 
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