\(tan3a-tan2a-tana=\frac{sin3a}{cos3a}-\frac{sin2a}{cos2a}-\frac{sina}{cosa}=\frac{sin3a.cos2a-sin2a.cos3a}{cos3a.cos2a}-\frac{sina}{cosa}\)

\(=\frac{sin\left(3a-2a\right)}{cos3a.cos2a}-\frac{sina}{cosa}=\frac{sina}{cos3a.cos2a}-\frac{sina}{cosa}=tana\left(\frac{cosa}{cos3a.cos2a}-1\right)\)

\(=tana\left(\frac{cos\left(3a-2a\right)-cos3a.cos2a}{cos3a.cos2a}\right)=tana\left(\frac{cos3a.cos2a+sin3a.sin2a-cos3a.cos2a}{cos3a.cos2a}\right)\)

\(=tana\left(\frac{sin3a.sin2a}{cos3a.cos2a}\right)=tana.tan2a.tan3a\)

Chọn B.

Ta có cot³a + tan³a = ( tan a + cota) ³- 3tan a.cot a ( cot a + tan a)

= m³ - 3.1.m = m³ - 3m

\(\tan^2\alpha-\sin^2\alpha\cdot\tan^2\alpha\)

\(=\tan^2\alpha\cdot\left(1-\cos^2\alpha\right)\)

\(=\tan^2\alpha\cdot\left(1-\cos\alpha\right)\left(1+\cos\alpha\right)\)

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

4

Đề sai rồi bạn ơi, mình không biết các loại máy khác bấm như nào nhma mình dùng fx 580 thì mode B xét đúng/sai thì máy cho kết quả là biểu thức này sai nha :v

\(VT=tanA+tanB+tanC=\dfrac{sinA}{cosA}+\dfrac{sinB}{cosB}+\dfrac{sinC}{cosC}\\ =\dfrac{sinA.sinB+cosA.cosB}{cosA+cosB}+\dfrac{sinC}{cosC}\\ =\dfrac{sin\left(A+B\right)}{cosA.cosB}+\dfrac{sinC}{cosC}\)

Theo định lý tổng 3 góc trong tam giác :

\(\widehat{A}+\widehat{B}+\widehat{C}=180^o\)

\(\Rightarrow A+B=180^o-C\\ \Leftrightarrow sin\left(A+B\right)=sin\left(180^o-C\right)=sinC\\ =\dfrac{sinC}{cosAcosB}+\dfrac{sinC}{cosC}\\ =\dfrac{sinC}{cosAcosBcosC}\left(cosC+cosAcosB\right)\\ =\dfrac{sinC}{cosAcosBcosC}\left(-cos\left(A+B\right)+cosAcosB\right)\\ =\dfrac{sinC}{cosAcosBcosC}\left(-cosAcosB+sinAsinB+cosAcosB\right)\\ =\dfrac{sinAsinBsinC}{cosAcosBcosC}\\ =\dfrac{sinA}{cosA}.\dfrac{sinB}{cosB}.\dfrac{sinC}{cosC}=tanA.tanB.tanC=VP\left(đpcm\right)\)

\(\left(cota+tana\right)^2-\left(cota-tana\right)^2\)

\(=cot^2a+tan^2a+2tana.cota-cot^2a-tan^2a+2tana.cota\)

\(=4tana.cota=4\)