Question

Tính giá trị các biểu thức sau:

a) $A=\sin ^{2} 3^{\circ}+\sin ^{2} 15^{\circ}+\sin ^{2} 75^{\circ}+\sin ^{2} 87^{\circ}$.

b) $B=\cos 0^{\circ}+\cos 20^{\circ}+\cos 40^{\circ}+\ldots+\cos 160^{\circ}+\cos 180^{\circ}$.

c) $C=\tan 5^{\circ} \tan 10^{\circ} \tan 15^{\circ} \ldots \tan 80^{\circ} \tan 85^{\circ}$.

 

Answer 1

a) Ta có: \(sin^2x+sin^2\left(90-x\right)=sin^2x+cos^2x=1.\)

áp dụng: A = 2

b)Ta có: \(cos\left(x\right)=-cos\left(180-x\right)\)

áp dụng: B = 0

c) Ta có: \(tan\left(x\right)\cdot tan\left(90-x\right)=\frac{sinx}{cosx}\cdot\frac{sin\left(90-x\right)}{cos\left(90-x\right)}=\frac{sinx}{cosx}\cdot\frac{cosx}{sinx}=1\)

áp dụng: C = 1

Answer 2

quá sai

Answer 3

trả dép em về

Answer 4

a) A=\left(\sin ^{2} 3^{\circ}+\sin ^{2} 87^{\circ}\right)+\left(\sin ^{2} 15^{\circ}+\sin ^{2} 75^{\circ}\right)A=(sin23∘+sin287∘)+(sin215∘+sin275∘)

\begin{aligned} &=\left(\sin ^{2} 3^{\circ}+\cos ^{2} 3^{\circ}\right)+\left(\sin ^{2} 15^{\circ}+\cos ^{2} 15^{\circ}\right) \\ &=1+1=2. \end{aligned}​=(sin23∘+cos23∘)+(sin215∘+cos215∘)=1+1=2.​

b) B=\left(\cos 0^{\circ}+\cos 180^{\circ}\right)+\left(\cos 20^{\circ}+\cos 160^{\circ}\right)+\ldots+\left(\cos 80^{\circ}+\cos 100^{\circ}\right)B=(cos0∘+cos180∘)+(cos20∘+cos160∘)+…+(cos80∘+cos100∘)

\begin{aligned} &=\left(\cos 0^{\circ}-\cos 0^{\circ}\right)+\left(\cos 20^{\circ}-\cos 20^{\circ}\right)+\ldots+\left(\cos 80^{\circ}-\cos 80^{\circ}\right) \\ &=0. \end{aligned}​=(cos0∘−cos0∘)+(cos20∘−cos20∘)+…+(cos80∘−cos80∘)=0.​

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Answer 5

  

Answer 6