Question

2sinx+15cos^2x is equal to 7. find tanx

Answer 1

see here in the solution.

Answer 2

$\tan x=\dfrac{4}{3}$

Explanation:

We have,

$2\sin x+15\cos^2 x = 7$

To find, $\tan x=?$

∴ $2\sin x+15(1-\sin^2 x) = 7$

⇒ $2\sin x+15-15\sin^2 x = 7$

⇒ $15\sin^2 x-2\sin x-8 =0$

⇒ $15\sin^2 x-12\sin x+10\sin x-8 =0$

⇒$3\sin x(5\sin x-4)+2(5\sin x-4)=0$

⇒ $(5\sin x-4)(3\sin x+2)=0$

⇒ $(5\sin x-4)=0 or,(3\sin x+2)=0$

⇒ $5\sin x-4=0$

⇒ $\sin x=\dfrac{4}{5}$

⇒ $\sin x=-\dfrac{2}{3}$ (neglect negative sign)

⇒ $\sin x=\dfrac{4}{5}=\dfrac{p}{b}$

p = perpendicular, h = hypotaneous

∴ Base, $b=\sqrt{h^{2}-p^{2}} =\sqrt{5^{2}-4^{2}}=\sqrt{9} =3$

∴ $\tan x=\dfrac{p}{b}=\dfrac{4}{3}$