\(A=\left(sin^2a+cos^2a\right)^2=1\)
\(B=sin^4a+cos^4a-2\cdot sin^2a\cdot cos^2a+2\cdot sin^2a\cdot cos^2a\)
\(=sin^4a+cos^4a\)
c: \(C=\left(sin^2a+cos^2a\right)^2-3\cdot sin^2a\cdot cos^2a\left(sin^2a+cos^2a\right)+3\cdot sin^2a\cdot cos^2a\)
=1-3+3=1
Rút gọn:
A= \(\sin^6\alpha+cos^6\alpha+3sin^2\alpha.cos^2\alpha\)
B= \(\left(cos\alpha-sin\alpha\right)^2+\left(cos\alpha+sin\alpha\right)^2\)
C= \(\dfrac{\left(cos\alpha-sin\alpha\right)^2-\left(cos\alpha+sin\alpha\right)^2}{sin\alpha.cos\alpha}\)
\(sin^6\alpha+cos^6\alpha+3sin^2\alpha.cos^2\alpha\)(với α là góc nhọn)
Chứng minh:
a)\(\cos^4\alpha-sin^4\alpha=2cos^2\alpha-1\)
b)\(\frac{cos\alpha}{1-sin\alpha}=\frac{1+sin\alpha}{cos\alpha}\)
c)\(\frac{\left(sin\alpha+cos\alpha\right)^2-\left(sin\alpha-cos\alpha\right)^2}{sin\alpha.cos\alpha}=4\)
Mình cần gấp!!!
Tính B = \(\sin^6\alpha+cos^6\alpha+3sin^2\alpha.cos^2\alpha\)
Hãy đơn giản các biểu thức:
a) \(1-sin^2\alpha\)
b) \(\left(1-cos\alpha\right)\left(1+cos\alpha\right)\)
c) \(1+sin^2\alpha+cos^2\alpha\)
d) \(sin\alpha-sin\alpha cos^2\alpha\)
e) \(sin^4\alpha+cos^4\alpha+2sin^2\alpha cos^2\alpha\)
g) \(tan^2\alpha-sin^2\alpha.tan^2\alpha\)
h)\(cos^2\alpha+tan^2\alpha.cos^2\alpha\)
i) \(tan^2\alpha\left(2cos^2\alpha+sin^2\alpha-1\right)\)
rút gọn
a)A=\(\frac{1+2cos\alpha.sin\alpha}{cos^2\alpha-sin^2\alpha}\)
b)B=\(\left(1+\cot^2\alpha\right)\left(1-sin^2\alpha\right)\)-\(\left(1+\cot^2\alpha\right)\left(1-\cos^2\alpha\right)\)
c)C=\(\sin^6\alpha+\cos^6\alpha\)+\(3\sin^2\alpha.cos^2\alpha\)
Rút gọn biểu thức
\(A=\frac{sin^2\alpha-cos^2\alpha}{1+2sin\alpha.cos\alpha}\)
\(\frac{1-2sin\alpha.cos\alpha}{sin^2\alpha-cos^2\alpha}\)
rút gọn biểu thức trên
C/m \(\forall\alpha< 45^0\)thì ta có\(\sin2\alpha=2sin\alpha.cos\alpha\)và \(cos2\alpha=cos^2\alpha-sin^2\alpha\)
2)đơn giản biểu thức
a) 1-sin2 alpha
b) sin4 alpha + cos4 alpha +2 sin2 alpha.cos2 alpha
c) (1-cos alpha).(1+cos alpha)
d) 1+ sin2 alpha +cos2 alpha
e) tg2 alpha -sin2 alpha.tg2 alpha
g) cos2 alpha+cos2 alpha.tg2 alpha
