Question

If 5cosA=3 then Sina+cosa/sinA-cosa=

Answer 1

Answer:-

$\\ \sf\longmapsto 5cosA=3$

$\\ \bf\longmapsto cosA=\dfrac{3}{5}$

We know

$\boxed{\star\sf sinA=\sqrt{1-cos^2A}}$

$\\ \sf\longmapsto sinA=\sqrt{1-(\dfrac{3}{5})^2}$

$\\ \sf\longmapsto sinA=\sqrt{1-\dfrac{9}{25}}$

$\\ \sf\longmapsto sinA=\sqrt{\dfrac{25-9}{25}}$

$\\ \sf\longmapsto sinA=\sqrt{\dfrac{16}{25}}$

$\\ \bf\longmapsto sinA=\dfrac{4}{5}$

Now

$\\ \sf\longmapsto \dfrac{sinA+cosA}{sinA-cosA}$

$\\ \sf\longmapsto \dfrac{\dfrac{4}{5}+\dfrac{3}{5}}{\dfrac{4}{5}-\dfrac{3}{5}}$

$\\ \sf\longmapsto \dfrac{\dfrac{4+3}{5}}{\dfrac{4-3}{5}}$

$\\ \sf\longmapsto \dfrac{\dfrac{7}{5}}{\dfrac{1}{5}}$

$\\ \sf\longmapsto \dfrac{7}{1}$

$\\ \sf\longmapsto 7$