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Ta có: \(\tan^240^0\cdot\sin^250^0-3+\left(1-\sin40^0\right)\left(1+\sin40^0\right)\)
\(=\tan^240^0\cdot\cos^240^0-3+1-\sin^240^0\)
\(=-2\)
Ta có: \(\tan^240^0\cdot\sin^250^0-3+\left(1-\sin40^0\right)\left(1+\sin40^0\right)\)
\(=\sin^240^0-3+1-\sin^240^0\)
=-2
a: \(2\sqrt{45}+\sqrt{5}-3\sqrt{80}\)
\(=6\sqrt{5}+\sqrt{5}-12\sqrt{5}\)
\(=-5\sqrt{5}\)
b: \(\sqrt{\left(2-\sqrt{3}\right)^2}+\dfrac{2}{\sqrt{3}+1}-6\sqrt{\dfrac{16}{3}}\)
\(=2-\sqrt{3}+\sqrt{3}-1-8\sqrt{3}\)
\(=-8\sqrt{3}+1\)
\(=\dfrac{\sin^240^0}{\cos^240^0}\cdot\cos^240^0-3+1-\sin^240^0=\sin^240^0-\sin^240^0-2=-2\)
b) Ta có: \(\sqrt{\left(2-\sqrt{3}\right)^2}+\dfrac{2}{\sqrt{3}+1}-6\sqrt{\dfrac{16}{3}}\)
\(=2-\sqrt{3}+\sqrt{3}-1-6\cdot\dfrac{4}{\sqrt{3}}\)
\(=1-8\sqrt{3}\)
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: \(sin^2+cos^2=1\)
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
\(=tan^240^0\cdot cos^240^0-3+1-sin^240^0\)
\(=sin^240^0-sin^240^0-2\)
=-2