a.

\(\left(sin^2\dfrac{x}{2}+cos^2\dfrac{x}{2}\right)^2-2sin^2\dfrac{x}{2}cos^2\dfrac{x}{2}=\dfrac{1}{2}\)

\(\Leftrightarrow2-\left(2sin\dfrac{x}{2}cos\dfrac{x}{2}\right)^2=1\)

\(\Leftrightarrow1-sin^2x=0\)

\(\Leftrightarrow cos^2x=0\)

\(\Leftrightarrow x=\dfrac{\pi}{2}+k\pi\)

b.

\(\left(sin^2x+cos^2x\right)^3-3sin^2x.cos^2x\left(sin^2x+cos^2x\right)=\dfrac{7}{16}\)

\(\Leftrightarrow1-\dfrac{3}{4}\left(2sinx.cosx\right)^2=\dfrac{7}{16}\)

\(\Leftrightarrow16-12.sin^22x=7\)

\(\Leftrightarrow3-4sin^22x=0\)

\(\Leftrightarrow3-2\left(1-cos4x\right)=0\)

\(\Leftrightarrow cos4x=-\dfrac{1}{2}\)

\(\Leftrightarrow4x=\pm\dfrac{2\pi}{3}+k2\pi\)

\(\Leftrightarrow x=\pm\dfrac{\pi}{6}+\dfrac{k\pi}{2}\)

c.

\(\left(sin^2x+cos^2x\right)^3-3sin^2x.cos^2x\left(sin^2x+cos^2x\right)=cos^22x+\dfrac{1}{4}\)

\(\Leftrightarrow1-\dfrac{3}{4}\left(2sinx.cosx\right)^2=cos^22x+\dfrac{1}{4}\)

\(\Leftrightarrow3-3sin^22x=4cos^22x\)

\(\Leftrightarrow3=3\left(sin^22x+cos^22x\right)+cos^22x\)

\(\Leftrightarrow3=3+cos^22x\)

\(\Leftrightarrow cos2x=0\)

\(\Leftrightarrow x=\dfrac{\pi}{4}+\dfrac{k\pi}{2}\)

Ta có :

\(\cos \left( {a + b} \right)\cos \left( {a - b} \right) = \frac{1}{2}\left( {\cos 2a + \cos 2b} \right) = \frac{1}{2}\left( {2{{\cos }^2}a - 1 + 2{{\cos }^2}b - 1} \right) = 0\)

Chọn A

Cây a, bạn nhân cả 2 vế với 3

Lấy vế nhân với 3 trừ đi ban đầu tất cả chia 2

b) Tính như bình thường

Câu c hình như sai đề

a) \(1-\frac{1}{3^{101}}\)

Câu c đúng đề bạn ạ, mình nhầm, ngại viết lắm

C = \(\dfrac{\dfrac{1}{9}-\dfrac{5}{6}-4}{\dfrac{7}{12}-\dfrac{1}{36}-10}\)

C = \(\dfrac{\dfrac{6-45-216}{54}}{\dfrac{21-1-360}{36}}\)

C = \(\dfrac{\dfrac{-85}{18}}{-\dfrac{85}{9}}\)

C = \(\dfrac{1}{2}\)

giúp với ạ

giải dc nhưng mà hoi lâu

a)\(\dfrac{5}{7}+\dfrac{4}{9}=\dfrac{45}{63}+\dfrac{28}{63}=\dfrac{73}{63}\) ; \(\dfrac{9}{11}+\dfrac{3}{8}=\dfrac{72}{88}+\dfrac{33}{88}=\dfrac{105}{88}\)

\(\dfrac{4}{5}-\dfrac{2}{3}=\dfrac{12}{15}-\dfrac{10}{15}=\dfrac{2}{15}\); \(\dfrac{16}{25}-\dfrac{2}{5}=\dfrac{16}{25}-\dfrac{10}{25}=\dfrac{6}{25}\)

\(\begin{array}{l}1,2.\frac{{15}}{4} + \frac{{16}}{7}.\frac{{ - 85}}{8} - 1,2.5\frac{3}{4} - \frac{{16}}{7}.\frac{{ - 71}}{8}\\ =(1,2.\frac{{15}}{4} - 1,2.5\frac{3}{4}) +( \frac{{16}}{7}.\frac{{ - 85}}{8}- \frac{{16}}{7}.\frac{{ - 71}}{8}) \\= \frac{{12}}{{10}}.\frac{{15}}{4} - \frac{{12}}{{10}}.\frac{{23}}{4} + \frac{{16}}{7}.\frac{{ - 85}}{8} - \frac{{16}}{7}.\frac{{ - 71}}{8}\\ = \frac{6}{5}.\frac{{15}}{4} - \frac{6}{5}.\frac{{23}}{4} + \frac{{16}}{7}.\frac{{ - 85}}{8} + \frac{{16}}{7}.\frac{{71}}{8}\\ = \frac{6}{5}.(\frac{{15}}{4} - \frac{{23}}{4}) + \frac{{16}}{7}.(\frac{{ - 85}}{8} + \frac{{71}}{8})\\ = \frac{6}{5}.\frac{{ - 8}}{4} + \frac{{16}}{7}.\frac{{ - 14}}{8}\\ = \frac{6}{5}.( - 2) + ( - 4)\\ = \frac{{ - 12}}{5} + \frac{{ - 20}}{5}\\ = \frac{{ - 32}}{5}\end{array}\)

Chú ý: Nếu phân số chưa tối giản, ta nên tối giản phân số trước để việc tính toán được thuận tiện hơn.