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Question Number 26778 by tawa tawa last updated on 29/Dec/17

$$\mathrm{If}\sin \left(\mathrm{A}\right)+\sin \left(\mathrm{B}\right)=\mathrm{p}\mathrm{and}\cos \left(\mathrm{A}\right)+\cos \left(\mathrm{B}\right)=\mathrm{q}$$$$\mathrm{show}\mathrm{that}\tan \left(\mathrm{A}\right)+\tan \left(\mathrm{B}\right)=\frac{8\mathrm{pq}}{{({\mathrm{p}}^2+{\mathrm{q}}^2)}^2-{4\mathrm{q}}^2}$$

Commented by tawa tawa last updated on 29/Dec/17

$$\mathrm{I}\mathrm{have}\mathrm{changed}\mathrm{the}\mathrm{question}\mathrm{sir}.$$

Answered by ajfour last updated on 29/Dec/17

$$\tan A+\tan B=$$$$\frac{[2-{(p-q)}^2](p^2+q^2)}{(p^2+1)(p^2+q^2)-4p^2}.$$

Commented by tawa tawa last updated on 29/Dec/17

$$\mathrm{please}\mathrm{prove}\mathrm{this}.\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.$$

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