Toán Lớp 9: Chứng minh rằng 1 + tan² a = 1/cos² a , 1+ cot² a = 1/ sin² a

Question

Toán Lớp 9:  Chứng minh rằng 1 + tan² a  = 1/cos² a , 1+ cot² a = 1/ sin² a

lanhuongthu · Answer

~rai~        (a)1+ tan^2 alpha= dfrac{1}{ cos^2 alpha}   text{X&eacute;t VP =} dfrac{1}{ cos^2 alpha}   quad quad quad= dfrac{ sin^2 alpha+ cos^2 alpha}{ cos^2 alpha}   quad quad quad= dfrac{ sin^2 alpha}{ cos^2 alpha}+ dfrac{ cos^2 alpha}{ cos^2 alpha}   quad quad quad= tan^2 alpha+1=VT.   Rightarrow 1+ tan^2 alpha= dfrac{1}{ cos^2 alpha}  b)1+ cot^2 alpha= dfrac{1}{ sin^2 alpha}   text{X&eacute;t VP=} dfrac{1}{ sin^2 alpha}   quad quad quad= dfrac{ sin^2 alpha+ cos^2 alpha}{ sin^2 alpha}   quad quad quad= dfrac{ sin^2 alpha}{ sin^2 alpha}+ dfrac{ cos^2 alpha}{ sin^2 alpha}   quad quad quad=1+ cot^2 alpha=VT.   Rightarrow 1+ cot^2 alpha= dfrac{1}{ sin^2 alpha}   text{Những c&ocirc;ng thức đ&atilde; d&ugrave;ng để chứng minh:}   sin^2 alpha+ cos^2 alpha=1; dfrac{ sin alpha}{ cos alpha}= tan alpha; dfrac{ cos alpha}{ sin alpha}= cot alpha. )

khanhngantoan · Answer

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