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cos 50=sin 40(2 góc phụ nhau)
50>40=>sin 50> sin 40=> sin 50> cos 50 (1)
sin 50<1 (2)
tan 50 =sin50/cos 50=sin50 / sin40 > 1(tử lớn hơn mẫu)=>tan 50>1 (3)
(1)(2)(3)=> tan50>sin50>cos50
a: \(\sin25^0< \sin70^0\)
b: \(\cos40^0>\cos75^0\)
c: \(\sin38^0=\cos52^0< \cos27^0\)
d: \(\sin50^0=\cos40^0>\cos50^0\)
Ta có: \(\sin10^0+\sin40^0-\cos50^0-\cos80^0\)
\(=\left(\sin10^0-\cos80^0\right)+\left(\sin40^0-\cos50^0\right)\)
\(=\left(\cos80^0-\cos80^0\right)+\left(\cos50^0-\cos50^0\right)\)
\(=0\)
a) \(sin40^o-cos50^o=cos50^o-cos50^o=0\)
b) \(sin^230^o+sin^240^o+sin^250^o+sin^260^o\)
= \(sin^230^o+sin^260^o+sin^240^o+sin^250^o\)
= \(sin^230^o+cos^230^o+sin^240^o+cos^240^o\)
= \(1+1=2\)
a) Gợi ý: Hai góc phụ nhau thì có sin góc này bằng cos góc kia.
vd: \(sin30^o=cos70^o\)
b) Gợi ý: \(sin^2+cos^2=1\)
Giải:
\(A=\sin10+\sin40-\cos50-\cos80\)
\(\Leftrightarrow A=\cos80+\cos50-\cos50-\cos80\)
\(\Leftrightarrow A=0\)
Vậy ...
\(B=\cos15+\cos25-\sin65-\sin75\)
\(\Leftrightarrow B=\sin75+\sin65-\sin65-\sin75\)
\(\Leftrightarrow B=0\)
Vậy ...
\(C=\dfrac{\tan27.\tan63}{\cot63.\cot27}\)
\(\Leftrightarrow C=\dfrac{\tan27.\tan63}{\tan27.\tan63}\)
\(\Leftrightarrow C=1\)
Vậy ...
\(D=\dfrac{\cot20.\cot45.\cot70}{\tan20.\tan45.\tan70}\)
\(\Leftrightarrow D=\dfrac{\cot20.\cot45.\cot70}{\cot70.\cot45.\cot20}\)
\(\Leftrightarrow D=1\)
Vậy ...
A= \(\frac{1}{2}\)[sin(-10)+sin90] +\(\frac{1}{2}\)(sin10+sin90)
A= \(\frac{1}{2}\)(-sin10 +1) +\(\frac{1}{2}\)(sin10 +1)
A=\(\frac{1}{2}\)(-sin10+sin10)+1
A= 1