(sin 1 độ + sin 2 độ + ... + sin 89 độ) - (cos 1 độ + cos 2 độ + ... + cos 89 độ)

=(cos 89 độ +... + cos 2 độ +cos 1 độ) - (cos 1 độ + cos 2 độ + ... + cos 89 độ)

=0

a) ta có : \(A=tan1.tan2.tan3...tan89\)

\(=\left(tan1.tan89\right).\left(tan2.tan88\right).\left(tan3.tan87\right)...\left(tan44.tan46\right).tan45\)

\(=\left(tan1.tan\left(90-1\right)\right).\left(tan2.tan\left(90-2\right)\right).\left(tan3.tan\left(90-3\right)\right)...\left(tan44.tan\left(90-44\right)\right).tan45\)

b) ta có \(B=\dfrac{sin\alpha+2cos\alpha}{3sin\alpha-4cos\alpha}=\dfrac{\dfrac{sin\alpha}{cos\alpha}+\dfrac{2cos\alpha}{cos\alpha}}{\dfrac{3sin\alpha}{cos\alpha}-\dfrac{4cos\alpha}{cos\alpha}}\)

\(=\dfrac{tan\alpha+2}{3tan\alpha-4}=\dfrac{\dfrac{1}{2}+2}{\dfrac{3}{2}-4}=-1\)

ta có \(D=\dfrac{2sin^2\alpha-3cos^2\alpha}{4cos^2\alpha-5sin^2\alpha}=\dfrac{\dfrac{2sin^2\alpha}{cos^2\alpha}-\dfrac{3cos^2\alpha}{cos^2\alpha}}{\dfrac{4cos^2\alpha}{cos^2\alpha}-\dfrac{5sin^2\alpha}{cos^2\alpha}}\)

\(=\dfrac{2tan^2\alpha-3}{4-5tan^2\alpha}=\dfrac{2\left(\dfrac{1}{2}\right)^2-3}{4-5\left(\dfrac{1}{2}\right)^2}=\dfrac{-10}{11}\)

Ta có: \(\tan^240^0\cdot\sin^250^0-3+\left(1-\sin40^0\right)\left(1+\sin40^0\right)\)

\(=\tan^240^0\cdot\cos^240^0-3+1-\sin^240^0\)

\(=-2\)

a: 

b: \(B=3-sin^290^0+2\cdot cos^260^0-3\cdot tan^245^0\)

\(=3-1+2\cdot\left(\dfrac{1}{2}\right)^2-3\cdot1^2\)

\(=2-3+2\cdot\dfrac{1}{4}=-1+\dfrac{1}{2}=-\dfrac{1}{2}\)

c: \(C=sin^245^0-2\cdot sin^250^0+3\cdot cos^245^0-2\cdot sin^240^0+4\cdot tan55\cdot tan35\)

\(=\left(\dfrac{\sqrt{2}}{2}\right)^2+3\cdot\left(\dfrac{\sqrt{2}}{2}\right)^2-2\cdot\left(sin^250^0+sin^240^0\right)+4\)

\(=\dfrac{1}{2}+3\cdot\dfrac{1}{2}-2+4\)

\(=2-2+4=4\)

Ta có : \(\sin^244+\sin^246+tan18+tan72\)

\(=\sin^244+\cos^244+\tan18+\cot18\)

\(=1+\dfrac{\sin^218+\cos^218}{\sin18.\cos18}=1+\dfrac{1}{\sin18.\cos18}\)

Vậy ...

- Ấn vô đây để soạn công thức toán nha .

A=(sin​​​²20°+sin²70°)+(sin²30°+sin²60°)

+(sin²40°+sin²50°)-tan²45°

=(sin​​²20°+cos​²20°)+(sin²30°+cos²30°)+(sin²40°+cos²40°)-1

=1+1+1-1=2

kết quả là 2