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Question Number 117259 by bemath last updated on 10/Oct/20

Answered by Dwaipayan Shikari last updated on 10/Oct/20

$$tan\alpha +tan\beta =3$$$$tan\alpha tan\beta =-3$$$$tan(\alpha +\beta )=\frac{tan\alpha +tan\beta }{1-tan\alpha tan\beta }=\frac{3}{4}$$$$sin(\alpha +\beta )=\frac{3}{5},cos(\alpha +\beta )=\frac{4}{5}$$$$\mid {sin}^2(\alpha +\beta )-3sin(\alpha +\beta )cos(\alpha +\beta )-3{cos}^2(\alpha +\beta )\mid$$$$=\mid \frac{9}{25}-\frac{36}{25}-\frac{48}{25}\mid =\mid -\frac{75}{25}\mid =3$$

Commented by bemath last updated on 10/Oct/20

$$\mathrm{santuyyy}$$

Answered by bemath last updated on 10/Oct/20

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