Question

cos2α +cos2β+cos2γ = 3, then sin2α+sin2β+sin2 γ =?
answer with steps pls ​

Answer 1

Answer

• $\sf cos^2\alpha+cos^2\beta+cos^2\gamma=3$

$\\ \sf\longmapsto cos^2(\alpha+\beta+\gamma)=3$

Now

$\boxed{\sf sin^2\theta=1-cos^2\theta}$

$\\ \sf\longmapsto sin^2\alpha+sin^2\beta+sin^2\gamma$

$\\ \sf\longmapsto sin^2(\alpha+\beta+\gamma)$

$\\ \sf\longmapsto 1-cos^2(\alpha+\beta+\gamma)$

$\\ \sf\longmapsto 1-3$

$\\ \sf\longmapsto -2$

$\sf\therefore sin^2\alpha+sin^2\beta+sin^2\gamma=-2.$