Question

Chứng minh rằng : 

a) \(\sin\left(270^0-\alpha\right)=-\cos\alpha\)

b) \(\cos\left(270^0-\alpha\right)=-\sin\alpha\)

c) \(\sin\left(270^0+\alpha\right)=-\cos\alpha\)

d) \(\cos\left(270^0+\alpha\right)=\sin\alpha\)

Answer 1

a) \(sin\left(270^o-\alpha\right)=sin\left(-90^o-\alpha\right)=-sin\left(90^o+\alpha\right)\)\(=-cos\alpha\).
b) \(cos\left(270^o-\alpha\right)=cos\left(-90^o-\alpha\right)=cos\left(90^o+\alpha\right)\)\(=-sin\alpha\).
c) \(sin\left(270^o+\alpha\right)=sin\left(-90^o+\alpha\right)=-sin\left(90^o-\alpha\right)\)\(=-cos\alpha\).
d) \(cos\left(270^o+\alpha\right)=cos\left(-90^o+\alpha\right)=cos\left(90^o-\alpha\right)\)\(=sin\alpha\).