sin a=1/4
=>sin^2a=1/16
=>cos^2a=15/16
\(B=\dfrac{3\cdot\dfrac{cosa}{sina}-\dfrac{sina}{cosa}}{2\cdot\dfrac{sina}{cosa}+\dfrac{cosa}{sina}}\)
\(=\dfrac{3\cdot cosa^2a-sin^2a}{sina\cdot cosa}:\dfrac{2\cdot sin^2a+cos^2a}{sina\cdot cosa}\)
\(=\dfrac{3\cdot cos^2a-sin^2a}{2\cdot sin^2a+cos^2a}\)
\(=\dfrac{3\cdot\dfrac{15}{16}-\dfrac{1}{16}}{2\cdot\dfrac{1}{16}+\dfrac{15}{16}}=\dfrac{44}{17}\)
7 cm đăng thức
a) \(\dfrac{tan\alpha-tan\beta}{cot\alpha-cot\alpha}=tan\alpha.cot\beta\)
b) \(tan100^o+\dfrac{sin530^o}{1+sin640^o}=\dfrac{1}{sin10^o}\)
c) 2(sin6α + cos6α) + 1 = 3(sin4α + cos4α)
Cho tanα = 2. Tính P=\(\dfrac{\tan\left(8\pi-\alpha\right)+2\cot\left(\pi+\alpha\right)}{3\tan\left(\dfrac{3\pi}{2}+\alpha\right)}\)
Cho 2tanα-cotα=1. Tính P=\(\dfrac{\text{tan ( 8 π − α ) + 2 cot ( π + α )}}{3\tan\left(\dfrac{3\pi}{2}+\alpha\right)}\)
6. CM đẳng thức
a) \(\dfrac{sin^3\alpha+cos^3\alpha}{sin\alpha+cos\alpha}=1-sin\alpha.cos\alpha\)
c) sin4α + cos4α - sin6α - cos6α = sin2α . cos2α
b) \(\dfrac{sin^2\alpha-cos^2\alpha}{1+2sin\alpha.cos\alpha}=\dfrac{tan\alpha-1}{tan\alpha+1}\)
CM đẳng thức
a) cos4α - sin4α = 2cos2α - 1
b) \(\dfrac{cos^2\alpha+tan^2\alpha-1}{sin^2\alpha}=tan^2\alpha\)
Rút gọn biểu thức
B = \(\dfrac{\cos\alpha}{\sqrt{2}}\).\(\sqrt{\dfrac{1}{1+\cos\alpha}+\dfrac{1}{1-\cos\alpha}}\)
Chứng minh : \(sin\left(\alpha-\pi\right)=-sin\alpha\)
giải các pt sau:
a, cot(x-\(\dfrac{\pi}{3}\))=1
b, tan(x+\(48^o\))=tan\(25^o\)
c, tan(x+\(\dfrac{3\pi}{4}\))=tan\(\dfrac{\pi}{7}\)
Với những giá trị nào của x, ta có mỗi đẳng thức sau :
a) \(\dfrac{1}{\tan x}=\cot x\)
b) \(\dfrac{1}{1+\tan^2x}=\cos^2x\)
c) \(\dfrac{1}{\sin^2x}=1+\cot^2x\)
d) \(\tan x+\cot x=\dfrac{2}{\sin2x}\)
