Respuesta :

Take RHS

[tex]\\ \rm\Rrightarrow \dfrac{tanA+tanB}{tanA-tanB}[/tex]

  • tanØ=sinØ/cosØ

[tex]\\ \rm\Rrightarrow \dfrac{\dfrac{sinA}{cosA}+\dfrac{sinB}{cosB}}{\dfrac{sinA}{cosA}-\dfrac{sinB}{cosB}}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{\dfrac{sinAcosB+cosAsinB}{cosAcosB}}{\dfrac{sinAcosB-cosAsinB}{cosAcosB}}[/tex]

  • cancel cosAcosB

[tex]\\ \rm\Rrightarrow \dfrac{sinAcosB+cosAsinB}{sinAcosB-cosAsinB}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{sin(A+B)}{sin(A-B)}[/tex]

Some important identities

[tex]\boxed{\begin{minipage}{6cm} Important Trigonometric identities :- \\ \\ $\: \: 1)\:\sin^2\theta+\cos^2\theta=1 \\ \\ 2)\:\sin^2\theta= 1-\cos^2\theta \\ \\ 3)\:\cos^2\theta=1-\sin^2\theta \\ \\ 4)\:1+\cot^2\theta=\text{cosec}^2 \, \theta \\ \\5)\: \text{cosec}^2 \, \theta-\cot^2\theta =1 \\ \\ 6)\:\text{cosec}^2 \, \theta= 1+\cot^2\theta \\\ \\ 7)\:\sec^2\theta=1+\tan^2\theta \\ \\ 8)\:\sec^2\theta-\tan^2\theta=1 \\ \\ 9)\:\tan^2\theta=\sec^2\theta-1$\end{minipage}}[/tex]

semsee45

Answer:

[tex]\boxed{\begin{minipage}{6 cm}\underline{Trigonometric Identities}\\\\$\sin (A \pm B)=\sin A \cos B \pm \cos A \sin B\\\\ \dfrac{\sin A}{\cos A}=\tan A$\\\end{minipage}}[/tex]

[tex]\dfrac{\sin (a+b)}{\sin (a-b)} & = \dfrac{\sin(a) \cos (b) + \cos (a) \sin (b)}{\sin(a) \cos (b) - \cos (a) \sin (b)}[/tex]

[tex]\dfrac{\sin (a+b)}{\sin (a-b)} & = \dfrac{\sin(a) \cos (b) + \cos (a) \sin (b)}{\sin(a) \cos (b) - \cos (a) \sin (b)} \times \dfrac{\dfrac{1}{\cos (a) \cos (b)}}{\dfrac{1}{\cos (a) \cos (b)}}[/tex]

[tex]\dfrac{\sin (a+b)}{\sin (a-b)} & = \dfrac{\dfrac{\sin(a) \cos (b)}{\cos (a) \cos (b)} + \dfrac{\cos (a) \sin (b)}{\cos (a) \cos (b)}}{\dfrac{\sin(a) \cos (b)}{\cos (a) \cos (b)} - \dfrac{\cos (a) \sin (b)}{\cos (a) \cos (b)}}[/tex]

[tex]\dfrac{\sin (a+b)}{\sin (a-b)} & = \dfrac{\dfrac{\sin(a)}{\cos (a)} + \dfrac{\sin (b)}{\cos (b)}}{\dfrac{\sin(a)}{\cos (a)} - \dfrac{\sin (b)}{\cos (b)}}[/tex]

[tex]\dfrac{\sin (a+b)}{\sin (a-b)}=\dfrac{\tan(a)+\tan(b)}{\tan(a)-\tan(b)}[/tex]

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