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 ...

\(F=cos^275^0-sin^275^0\)

\(=1-sin^275^0-sin^275^0\)

\(=1-2\cdot sin^275^0=cos150=-\dfrac{\sqrt{3}}{2}\)

a: \(cos\left(2x-\dfrac{\Omega}{6}\right)+cos\left(x+\dfrac{\Omega}{3}\right)=0\)

=>\(cos\left(2x-\dfrac{\Omega}{6}\right)+sin\left(\dfrac{\Omega}{6}-x\right)=0\)

=>\(cos\left(2x-\dfrac{\Omega}{6}\right)=-sin\left(\dfrac{\Omega}{6}-x\right)=sin\left(x-\dfrac{\Omega}{6}\right)\)

=>\(cos\left(2x-\dfrac{\Omega}{6}\right)=cos\left(\dfrac{\Omega}{2}-x+\dfrac{\Omega}{6}\right)\)

=>\(cos\left(2x-\dfrac{\Omega}{6}\right)=cos\left(-x+\dfrac{2}{3}\Omega\right)\)

=>\(\left[{}\begin{matrix}2x-\dfrac{\Omega}{6}=-x+\dfrac{2\Omega}{3}+k2\Omega\\2x-\dfrac{\Omega}{6}=x-\dfrac{2}{3}\Omega+k2\Omega\end{matrix}\right.\)

=>\(\left[{}\begin{matrix}3x=\dfrac{5}{6}\Omega+k2\Omega\\x=-\dfrac{1}{2}\Omega+k2\Omega\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{18}\Omega+\dfrac{k2\Omega}{3}\\x=-\dfrac{1}{2}\Omega+k2\Omega\end{matrix}\right.\)

b: \(cos\left(2x+30^0\right)+sin\left(x-30^0\right)=0\)

=>\(cos\left(2x+30^0\right)=-sin\left(x-30^0\right)\)

=>\(cos\left(2x+30^0\right)=sin\left(-x+30^0\right)\)

=>\(cos\left(2x+30^0\right)=cos\left(60^0+x\right)\)

=>\(\left[{}\begin{matrix}2x+30^0=x+60^0+k\cdot360^0\\2x+30^0=-x-60^0+k\cdot360^0\end{matrix}\right.\)

=>\(\left[{}\begin{matrix}x=30^0+k\cdot360^0\\3x=-90^0+k\cdot360^0\end{matrix}\right.\)

=>\(\left[{}\begin{matrix}x=30^0+k\cdot360^0\\x=-30^0+k\cdot120^0\end{matrix}\right.\)

a)
\(4a^2cos^260^o+2ab.cos^2180^o+\dfrac{4}{3}cos^230^o\)
\(=4a^2.\left(\dfrac{1}{2}\right)^2+2ab.\left(-1\right)^2+\dfrac{4}{3}.\left(\dfrac{\sqrt{3}}{2}\right)^2\)
\(=4a^2.\dfrac{1}{4}+2ab+\dfrac{4}{3}.\dfrac{3}{4}\)
\(=a^2+2ab+1\).
b)
\(\left(asin90^o+btan45^o\right)\left(acos0^o+bcos180^o\right)\)
\(=\left(a+b\right)\left(a-b\right)=a^2-b^2\).

a) Ta có: \(sin\alpha=cos\left(90-\alpha\right)\Rightarrow sin42=cos48\)

\(\Rightarrow sin42-cos48=0\)

b) Ta có: \(sin\alpha=cos\left(90-\alpha\right)\Rightarrow sin61=cos29\Rightarrow sin^261=cos^229\)

\(\Rightarrow sin^261+sin^229=sin^229+cos^229=1\)

c) Ta có: \(tan\alpha=\dfrac{1}{tan\left(90-\alpha\right)}\Rightarrow tan40=\dfrac{1}{tan50}\)

\(\Rightarrow tan40.tan50=1\) mà \(tan45=1\Rightarrow tan40.tan45.tan50=1\)

\(sin42^0-cos48^0=sin42^0-sin\left(90^0-48^0\right)=sin42^0-sin42^0=0\)

\(sin^261^0+sin^229^0=sin^261^0+cos^2\left(90^0-29^0\right)=sin^261^0+cos^261^0=1\)

\(tan40^0.tan50^0.tan45^0=tan40^0.cot\left(90^0-50^0\right).1=tan40^0.cot40^0=1\)

Sử dụng các công thức:

\(cosa=sin\left(90^0-a\right)\) ; \(sina=cos\left(90^0-a\right)\) ; \(tana=cot\left(90^0-a\right)\) ; \(tana.cota=1\)

\(\dfrac{1}{2-\dfrac{3}{4+\dfrac{5}{6-\dfrac{7}{8+\dfrac{9}{10}}}}}=\dfrac{1}{x+\dfrac{1}{3+\dfrac{1}{5}}}+\dfrac{1}{1+\dfrac{1}{1+\dfrac{1}{2}}}\\ \Leftrightarrow\dfrac{767}{1070}=\dfrac{1}{x+\dfrac{5}{16}}+\dfrac{3}{5}\\ \Leftrightarrow\dfrac{25}{214}=\dfrac{1}{x+\dfrac{5}{16}}\\ \Rightarrow x+\dfrac{5}{16}=\dfrac{214}{25}\Rightarrow x=\dfrac{3299}{400}\)

a: \(=\left(sin^210^0+sin^280^0\right)+\left(sin^220^0+sin^270^0\right)+sin^245^0\)

\(=1+1+\dfrac{1}{2}=\dfrac{5}{2}\)

b: \(=\left(sin^242^0+sin^248^0\right)+\left(sin^243^0+sin^247^0\right)+...+sin^245^0\)

=1+1+1+1/2

=3,5

c: \(=tan35^0\cdot tan55^0\cdot tan40^0\cdot tan50^0\cdot tan45^0=1\)

d: \(=\left(cos^215^0+cos^275^0\right)-\left(cos^225^0+cos^265^0\right)+\left(cos^235^0+cos^255^0\right)-\dfrac{1}{2}\)

=1-1+1-1/2

=1/2