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\(B=\sin^247^o\times\cos45^o+\sin45^o\times\cos^247^o\)
\(B=\sin^247^o\times\cos45^o+\cos45^o\times\cos^247^o\)
\(B=\cos45^o\left(\sin^247^o+\cos^247^o\right)\)
\(B=\cos45^o.1=\cos45^o\)
\(ADCT:\sin^2\alpha+\cos^2\alpha=1\)
\(A=\left(\sin^242^0+\sin^248^0\right)+\left(\sin^243^0+\sin^247^0\right)+\left(\sin^244^0+\sin^246^0\right)+\sin45^0\)
\(A=\left(\sin^242^0+\cos^242^0\right)+\left(\sin^243^0+\cos^243^0\right)+\left(\sin^244^0+\cos^244^0\right)+\frac{\sqrt{2}}{2}\)
\(A=1+1+1+\frac{\sqrt{2}}{2}=\frac{6+\sqrt{2}}{2}\)
Câu b lm tương tự
a, \(\cos^215+\cos^225+\cos^235+\cos^245+\sin^235+\sin^225+\sin^215\)
=\(\left(\cos^215+\sin^215\right)+\left(\cos^225+\sin^225\right)+\left(\cos^235+\sin^235\right)+\cos^245\)
=\(1+1+1+\frac{1}{2}=\frac{7}{2}\)
b.\(\sin^210-\sin^220-\sin^230-\sin^240-\cos^240-\cos^220+\cos^210\)
=\(\left(\sin^210+\cos^210\right)-\left(\sin^220+\cos^220\right)-\left(\sin^240+\cos^240\right)-\sin^230\)
=\(1-1-1-\frac{1}{4}=-\frac{5}{4}\)
c,\(\sin15+\sin75-\sin75-\cos15+\sin30=\sin30=\frac{1}{2}\)
\(=\left(1-sin^247^0\right)\cdot sin45^0+sin47^0\cdot\left(1-sin^245^0\right)\)
\(=sin45-sin^247^0\cdot\dfrac{\sqrt{2}}{2}+sin47^0-\dfrac{1}{2}\cdot sin47^0\)
\(\simeq0.69\)