a, Tìm được sinα = 24 5 , tanα = 24 , cotα =  1 24

b, cosα = 5 3 , tanα = 2 5 , cotα =  5 2

c, sinα = ± 2 5 , cosα = ± 1 5 , cotα =  1 2

d, sinα = ± 1 10 , cosα = ± 3 10 , tanα = 1 3

ta có :\(\sin2=\dfrac{\sqrt{3}}{2}\Rightarrow2=60^0\)

\(\cos60^o=\dfrac{1}{2};\tan60^o=\sqrt{3};\cot60^o=\dfrac{1}{\sqrt{3}}\)

a: \(\cos\alpha=\dfrac{1}{2}\)

\(\tan\alpha=\sqrt{3}\)

\(\cot\alpha=\dfrac{\sqrt{3}}{3}\)

Ta có:

\(cot\alpha\cdot tan\alpha=1\)

\(\Rightarrow cot\alpha=\dfrac{1}{tan\alpha}\)

\(\Rightarrow cota=\dfrac{1}{\dfrac{3}{4}}=\dfrac{4}{3}\)

Mà:

\(cot^2\alpha+1=\dfrac{1}{sin^2\alpha}\)

\(\Rightarrow sin\alpha=\sqrt{\dfrac{1}{cot^2\alpha+1}}\)

\(\Rightarrow sin\alpha=\sqrt{\dfrac{1}{\left(\dfrac{4}{3}\right)^2+1}}=\dfrac{3}{5}\) 

Lại có:

\(cos^2\alpha+sin^2\alpha=1\)

\(\Rightarrow cos\alpha=\sqrt{1-sin^2a}\)

\(\Rightarrow cos\alpha=\sqrt{1-\left(\dfrac{3}{5}\right)^2}=\dfrac{4}{5}\)

\(tan\alpha=\dfrac{3}{4}\\ \Rightarrow cot\alpha=1:\dfrac{3}{4}=\dfrac{4}{3}\)

Có:

\(1+cot^2\alpha=\dfrac{1}{sin^2\alpha}\\ \Rightarrow sin\alpha=\sqrt{1:\left(1+\left(\dfrac{4}{3}\right)^2\right)}=\dfrac{3}{5}\)

\(\Rightarrow cos\alpha=\sqrt{1-\left(\dfrac{3}{5}\right)^2}=\dfrac{4}{5}\)

Tương tự câu 2

Gợi ý: Sử dụng công thức:  sin 2 α + cos 2 α = 1

Ảnh 1 là bài 1,3. Ảnh 2 là bài 2 nhé bạn.

Bài 3: 

Ta có: \(A=\cos^220^0+\cos^240^0+\cos^250^0+\cos^270^0\)

\(=\left(\sin^270^0+\cos^270^0\right)+\left(\sin^250^0+\cos^250^0\right)\)

=1+1

=2

Cho α là góc nhọn, sinα = 1/2. Tính cosα; tanα; cotα

Ta có: sin 2 α + cos 2 α = 1

\(1+tan^2a=\dfrac{1}{cos^2a}=1:\dfrac{1}{25}=25\)

=>tan^2a=24

=>tana=2*căn 6

\(cota=\dfrac{1}{2\sqrt{6}}=\dfrac{\sqrt{6}}{12}\)

\(sina=\sqrt{1-\left(\dfrac{1}{5}\right)^2}=\dfrac{2\sqrt{6}}{5}\)