\(\frac{tan^3a}{sin^2a}-\frac{1}{sina.cosa}+\frac{cot^3a}{cos^2a}=\frac{1}{sin^2a}\left(tan^3a-tana+cot^3a.tan^2a\right)\)
\(=\frac{1}{sin^2a}\left(tan^3a-tana+cota\right)=\left(1+cot^2a\right)\left(tan^3a-tana+cota\right)\)
\(=tan^3a-tana+cota+cot^2a.tan^3a-cot^2a.tana+cot^3a\)
\(=tan^3a-tana+cota+tana-cota+cot^3a\)
\(=tan^3a+cot^3a\)
cho a,b,c >0 chứng minh
\(\frac{a}{2b+3c}+\frac{b}{2c+3a}+\frac{c}{2a+3b}\ge\frac{3}{5}\)
Cho \(\sin x=\frac{-1}{3}\).
Tính P=\(cos\left(2\pi-x\right).tan\left(\pi+x\right)-tan\left(\frac{\pi}{2}-x\right).cot\left(\pi-x\right)\).
Chứng minh :
(1 + tan x)cos2x + (1 + cot x)sin2x = (sin x + cos x)2
Chứng minh rằng: \(\frac{sin^2\alpha-cos^2\alpha}{1+2sin\alpha cos\alpha}=\frac{tan\alpha-1}{tan\alpha+1}\)
1. cho sinx + cosx = 1/2 . Tính sin3x + cos3x = ?
2. P = \(\frac{1-2sin^2x}{2cot\left(\frac{\pi}{4}+x\right)cos^2\left(\frac{\pi}{4}-x\right)}\)
3. cho tanx + cotx = 2 . Tính tan2x + cot2x
Cm các đẳng thức \
1, \(\frac{sin^4a+2sina.cosa-cos^4a}{tan2a-1}=cos2a\)
2, \(\frac{sin^23a}{sin^2a}-\frac{cos^23a}{cos^2a}=8cos^2a\)
3, \(sin9a+3sin7a+3sin5a+sin3a=8sin6a+cos^2a\)
Mọi người giúp em giải câu này với :Chứng minh rằng (Tan2x/1+tan2x)(1+cot2x/cotx)=1+tan4x/tan2x+cot2x
Chứng minh :
a) ( tan2x - tanx )cos 2x = tan x
b) 2(1-sinx)(1+cosx) = (1-sinx+cosx)2
c) 1 + cotx + cot2x + cot3x = cosx+sinx / sin3x
d) cos3x/sinx + sin3x/cosx = 2cot2x
Chứng minh
\(\frac{\left(sina+cosa\right)^2-1}{cota-sina.cosa}=2tan^2a\)
