\(tan\alpha+\frac{cos\alpha}{1+sin\alpha}=\frac{sin\alpha}{cos\alpha}+\frac{cos\alpha}{1+sin\alpha}=\frac{sin^2\alpha+sin\alpha+cos^2\alpha}{cos\alpha\left(1+sin\alpha\right)}=\frac{1+sin\alpha}{cos\alpha\left(1+sin\alpha\right)}=\frac{1}{cos\alpha}\)=>đpcm
Rút gọn biểu thức
\(E = cot(5π+α).cos(α-\dfrac{3π}{2})+cos(α-2π)-2.cos(\dfrac{π}{2}+α)\)\(D = sin(π+α)-cos(\dfrac{π}{2}-α)+cot(4π-α)+tan(\dfrac{5π}{2}-α)\)
Tính cos(α-π/3) biết sinα=3/5 và π/2
1/ \(\alpha\ne\frac{\pi}{2}+k\pi,k\in Z\) chứng minh rằng: \(\frac{\sin^2\alpha-\cos^2\alpha}{1+2\sin\cos}=\frac{\tan-1}{\tan+1}\)
chứng minh 1-tan^2x/1+tan^2x=cos^4x-sin^4x
Chứng minh đẳng thức
(tan^3x/sin^2x)-(1/sinx.cosx)+ (cot^3x/cos^2x)=tan^3x+cot^3x
Cho tam giác ABC chứng minh:
a)\(sin\frac{A}{2}=cos\frac{B}{2}.cos\frac{C}{2}-sin\frac{B}{2}sin\frac{C}{2}\)
b)\(\frac{tan^2A-tan^2B}{1-tan^2A.tan^2B}=-tan\left(A-B\right).tanC\)
c) cotA.cotB + cotB.cotC+cotC.cotA=1
chứng minh:
a) \(\frac{cos\left(a-b\right)}{sin\left(a+b\right)}=\frac{cota.cotb+1}{cota.cotb-1}\)
b) sin(a+b).sin(a-b)=\(sin^2a-sin^2b=cos^2a-cos^2b\)
c) cos(a+b).cos(a-b)=\(cos^2a-sin^2b=cos^2b-sin^2a\)
chứng minh (tan^2x-sin^2x)/(cot^2x-cos^2x)=tan^6x
cm các đẳng thức:
a) \(\frac{1+\sin^2\alpha}{1-\sin^2\alpha}=1+2\tan^2\alpha\)
b) \(\frac{\cos\alpha}{1+\sin\alpha}+\tan\alpha=\frac{1}{\cos\alpha}\)
c) \(\frac{\sin\alpha}{1+\cos\alpha}+\frac{1+\cos\alpha}{\sin\alpha}=\frac{2}{\sin\alpha}\)
