Question

if 2 sin theta +cos theta =2. find sin theta​

Answer 1

\sin{theta}\ = 1 or $\frac{3}{5}$

Step-by-step explanation:

Given,

2·\sin{theta}\ + \cos{theta}\ = 2

⇒ 2·\sin{theta}\ +  \$\1 - sqr^{2} theta}$ = 2

⇒    \$\1 -sqr^{2} theta}$ = 2 - 2·\sin{theta}\   ........ (1)

Squaring both sides in equation (1), we get

1 - sqr^{2} theta}[/tex] = 4 - 8\sin{theta}\ + 4sqr^{2} theta}[/tex]

⇒ 4sqr^{2} theta}[/tex] - 5\sin{theta}\ - 3\sin{theta}\ + 3 = 0

⇒ 5\sin{theta}\(\sin{theta}\ - 1) - 3(\sin{theta}\ - 1) = 0

⇒ (\sin{theta}\ - 1) (5\sin{theta}\ - 3) = 0

∴ \sin{theta}\ = 1 or $\frac{3}{5}$