\(sin15^o+sin75^o-cos15^o-cos75^o+sin30^o\)

\(=\left(sin15+sin75^o\right)-\left(cos15^o+cos75^o\right)+sin30^o\)

\(=\dfrac{\sqrt{6}}{2}-\dfrac{\sqrt{6}}{2}+\dfrac{1}{2}\)

\(=0+\dfrac{1}{2}\)

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

\(sin15^o+sin75^o-cos15^0-cos75^o+sin30^o\)

\(=cos75^o+cos15^0-cos15^0-cos75^o+sin30^o\)

\(=sin30^o=\dfrac{1}{2}\)

Biểu thức này chỉ rút gọn được khi mẫu là \(1-2sin^210^0\)

\(tan40+tan50=\dfrac{sin40}{cos40}+\dfrac{sin50}{cos50}=\dfrac{sin40.cos50+cos50.sin40}{cos40.cos50}\)

\(=\dfrac{sin\left(40+50\right)}{\dfrac{1}{2}\left(cos90+cos10\right)}=\dfrac{2}{cos10}\)

\(\Rightarrow tan30+tan60+tan40+tan50=\dfrac{\sqrt{3}}{3}+\sqrt{3}+\dfrac{2}{cos10}\)

\(=\dfrac{4\sqrt{3}}{3}+\dfrac{2}{cos10}=\dfrac{4\sqrt{3}cos10+6}{3.cos10}=\dfrac{4\sqrt{3}\left(cos10+\dfrac{\sqrt{3}}{2}\right)}{3.cos10}\)

\(=\dfrac{4\sqrt{3}\left(cos10+cos30\right)}{3cos10}=\dfrac{8\sqrt{3}cos20.cos10}{3cos10}=\dfrac{8\sqrt{3}}{3}cos20\)

\(\Rightarrow G=\dfrac{\dfrac{8\sqrt{3}}{3}cos20}{1-2sin^210}=\dfrac{\dfrac{8\sqrt{3}}{3}cos20}{cos20}=\dfrac{8\sqrt{3}}{3}\)

Ta có:

tan 89 0 = c o t 1 0 ; tan 88 0 = c o t 2 0 ; …; tan 46 0 = c o t 44 0 và tan   α . c o t   α = 1

Nên B = tan   1 0 . tan   89 0 . tan   2 0 . tan   88 0 … tan   46 0 . tan   44 0 . tan   45 0

=  tan   1 0 . c o t   1 0 . tan   2 0 . c o t   2 0 . tan   3 0 . c o t   3 0  …  tan   44 0 . c o t   44 0 . tan   45 0

= 1.1.1….1.1 = 1

Vậy B = 1

Đáp án cần chọn là: B

Chọn A.

Ta có: