Find s i n θ sin\theta

Level pending

If

2 s i n θ = 2 − c o s θ 2sin\theta =2-cos\theta

find s i n θ sin\theta

-3/5 1 or 3/5 -1 or 1 Cannot say

Soumo Mukherjee by Soumo Mukherjee , 25, India

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1 solution

Soumo Mukherjee
Oct 17, 2014

c o s θ = 2 − 2 s i n θ ⇒ 1 − sin ⁡ 2 θ = 2 − 2 s i n θ ⇒ 5 sin ⁡ 2 θ − 8 s i n θ + 3 = 0 ⇒ s i n θ = 1 o r 3 / 5 \displaystyle cos{ \theta }=2-2sin\theta \\ \Rightarrow \sqrt { 1-\sin ^{ 2 }{ \theta } } =2-2sin\theta \\ \Rightarrow 5\sin ^{ 2 }{ \theta } -8sin{ \theta }+3=0\\ \Rightarrow sin{ \theta }=1\quad or\quad 3/5

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