\(\Rightarrow2sin\left(\frac{\pi}{4}+2x\right)=\frac{3}{2}\) \(\Rightarrow sin\left(\frac{\pi}{4}+2x\right)=\frac{3}{4}\)
\(\Rightarrow sin\frac{\pi}{4}+sin2x=\frac{3}{4}\) \(\Rightarrow sin2x=\frac{3}{4}-sin\left(\frac{\pi}{4}\right)=0,74\)
\(\Rightarrow2x=48\Rightarrow x=\frac{48}{2}=24\)
Cho \(\sin\alpha+\cos\alpha=\frac{\sqrt{6}}{2},a\in\left(0;\frac{\pi}{4}\right)\)
Tính giá trị biểu thức: \(P=\cos\left(\alpha+\frac{\pi}{4}\right)+\sqrt{2\left(1-\sin\alpha\cos\alpha+\sin\alpha-\cos\alpha\right)}\)
Tìm tất cả các nghiệm của phương trình : \(\frac{2.sin\left(\frac{pi}{3}-2x\right)+2.sin2x+\sqrt{3}}{c\text{os}x}=4.c\text{os}4x\)
trên đoạn 50,55
Giúp mình với ạ. Giải pt:
1) \(sin^2x\left(x+\frac{\pi}{4}\right)=\sqrt{2}s\text{inx}\)
2) \(3\sqrt{2}c\text{os}x-s\text{inx}=c\text{os}3x+3\sqrt{2}sinxsin2x\:\)
rút gọn
\(C=\frac{\sqrt{2}\cos x-2\cos\left(\frac{\eta}{4}+x\right)}{-\sqrt{2}\sin x-2\sin\left(\frac{\eta}{4}+x\right)}\)
GPT
A,\(\sqrt{X+1}+\sqrt{4-X}+\sqrt{4+3X-X^2=5}\)
B,\(\sqrt{X^2-2X+5}=2-\left(X^2-1\right)^4\)
C,\(\left(X-5\right)^3=5\sqrt[3]{2X-9}-3X+6\)
D,\(\left(2X+1\right)\sqrt{\frac{X+1}{X}}=X+2+\sqrt[3]{2X^2+X^3}\)
MN ƠI GIÚP E MAI E ĐI HOK RỒI
ETICH CHO AI TRẢ LỜ NHANH NHẤT
RÚT GỌN:
1. \(4\sin xsin\left(x+\frac{\pi}{2}\right)sin\left(2x+\frac{\pi}{2}\right)\)
2 \(1-8\sin^2x\cos^2x\)
3 \(\frac{2}{\left(1-\tan a\right)\left(1+\cot a\right)}\)
4 \(\left(1-\tan^2a\right)\cot a\)
5 \(\cos^2\frac{\pi}{24}-\cos^4\frac{\pi}{24}\)
giải pt
a) \(\sin^2\left(\frac{x}{2}-\frac{\pi}{4}\right).tan^2x-cos^2\frac{x}{2}=0\)
b) \(3tan^3x-tanx+\frac{3\left(1+sinx\right)}{cos^2x}-8cos^2\left(\frac{\pi}{4}-\frac{x}{2}\right)=0\)
GPT\(\sqrt[4]{x}+\sqrt{x}+\sqrt[4]{1-x}+\sqrt{1-x}=2\left(\sqrt{\frac{1}{2}}+\sqrt[4]{\frac{1}{2}}\right)\) giải hộ cần gấp
\(\frac{6x-\left(x+6\right)\sqrt{x}-3}{2\left(x-4\sqrt{x}+3\right)\left(2-\sqrt{x}\right)}-\frac{3}{-2x+10\sqrt{x}-12}-\frac{1}{3\sqrt{x}-x-2}\)