Cho a là góc nhọn.Chứng minh:
a) 1/(1+tan a) + 1/(1+cos a) =1
b)sin^4 a-cos^4 a=2 sin^2 a-1
c)sin^2 a= tan^2 a / 1+tan^2 a
d)cos^2 a= 1/1+tan^2 a
Cho a là góc nhọn.Chứng minh:
a) 1/(1+tan a) + 1/(1+cos a) =1
b)sin^4 a-cos^4 a=2 sin^2 a-1
c)sin^2 a= tan^2 a / 1+tan^2 a
d)cos^2 a= 1/1+tan^2 a
a, không CM được.
b,
$VT=\sin^4a-\cos^4a$
$=(\sin^2a-\cos^2a)(\sin^2a+\cos^2a)$
$=\sin^2a-\cos^2a$
$=\sin^2a-1+\sin^2a$
$=2\sin^2a-1$
$=VP$
c,
$VP=\tan^2 a : (1+\tan^2a)$
$=\tan^2 a: (\dfrac{\cos^2a}{\cos^2a}+\dfrac{\sin^2a}{\cos^2a})$
$=\tan^2a : \dfrac{1}{\cos^2a}$
$=\dfrac{\sin^a}{\cos^2a}.\cos^2a$
$=\sin^2a$
$=VT$
d,
$VP=\dfrac{1}{1+\tan^2a}$
$=\dfrac{1}{\dfrac{\cos^2a}{\cos^2a}+\dfrac{\sin^2a}{\cos^2a}}$
$=\dfrac{1}{\dfrac{1}{\cos^2a}}$
$=\cos^2a$
$=VT$