Đặt \(A=sin6.cos12.cos24.cos48\)
\(\Rightarrow A.cos6=sin6.cos6.cos12.cos24.cos48\)
\(A.cos6=\frac{1}{2}sin12.cos12.cos24.cos48\)
\(A.cos6=\frac{1}{4}sin24.cos24.cos48=\frac{1}{8}sin48.cos48\)
\(A.cos6=\frac{1}{16}sin96=\frac{1}{16}cos6\)
\(\Rightarrow A=\frac{1}{16}\)
cos 0 + cos 20 + cos 40 +...+ cos 160 + cos 180
Biến đổi thành tích các biểu thức sau:
A = \(cos (x-30°) - cos (x - 60°)\)
B = \(1+cos x + cos 2x\)
C = \(4 cos^2x - 1\)
D = \(\sqrt{3} sin x - cos x\)
E = \(sin a + sin 2a + sin 3a + sin 4a\)
F = \(sin 70° + sin 50° - sin 20°\)
G = \(cos (60° + x) + cos (60° - x) + cos 3x\)
H = \(cos x + cos 2 x + cos 3 x\)
Tính P = \(\cos^20^0+\cos^21^0+\cos^22^0+...+\cos^2180^0\)
\(\sqrt{\sin^4x+4\cos^2x}+\sqrt{\cos^4x+4\sin^2x}\)
=\(\sqrt{\left(1-cos^2x\right)^2+4\cos^2x}+\sqrt{\left(1-sin^2x\right)^2+4\sin^2x}\)
=\(\sqrt{\cos^4x-2\cos^2x+1+4\cos^2x}+\sqrt{\sin^4x-2\sin^2x+1+4\sin^2x}\)
=\(\sqrt{\cos^4x+2\cos^2x+1}+\sqrt{\sin^4x+2\sin^2x+1}\)
=\(\sqrt{\left(cos^2x+1\right)^2}+\sqrt{\left(sin^2x+1\right)^2}\)
=\(cos^2x+1+sin^2x+1=3\)
rút gọn
\(\dfrac{\sin^2x-\cos^2x+\cos^4x}{\cos^2x-\sin^2x+\sin^4x}\)
sin(pi/7).B= cos(pi/7).cos(4pi/7).cos(5pi/7).tính gtri B?
tính giá trị biểu thức :
P= cos 200 +cos 400 +cos 600 +......+ cos 1800
Tính cos2(1.150)+cos2(3.150)+.....+cos2(9.150)+cos2(11.150)
Chứng minh rằng:
\(\sqrt{\dfrac{1+cos\alpha}{1-cos\alpha}}-\sqrt{\dfrac{1-cos\alpha}{1+cos\alpha}}=2cot\alpha\left(0< \alpha< \dfrac{\pi}{2}\right)\).
Tính a) sin^4α - cos^4α , biết cos2α=3/5
b) cos(α-β) biết sinα - sinβ = 1/3 và cosα - cosβ = 1/2
