Question

if 2 sin theeta -cos theeta=1
cos theeta + sin theeta
then the value of cot theeta is
a) 1/2
b) 1/3
c) 3
d) 2​

Answer 1

$2sinθ - cosθ = 1sinθ + cosθ$

→ $2sinθ - 1sinθ = cosθ + cosθ$

→ $sinθ = 2cosθ$

→ $\dfrac{sinθ }{cosθ} = 2$

→ $\dfrac{cosθ }{sinθ} = \dfrac {1}{2}$

$\therefore~ cot \theta = \dfrac{1}{2}$

Answer 2

$2sinθ−cosθ=1sinθ+cosθ</p><p></p><p>→ 2sinθ - 1sinθ = cosθ + cosθ2sinθ−1sinθ=cosθ+cosθ</p><p></p><p>→ sinθ = 2cosθsinθ=2cosθ</p><p></p><p>→ \dfrac{sinθ }{cosθ} = 2 </p><p>cosθ</p><p>sinθ</p><p> </p><p> =2</p><p></p><p>→ \dfrac{cosθ }{sinθ} = \dfrac {1}{2} </p><p>sinθ</p><p>cosθ</p><p> </p><p> = </p><p>2</p><p>1</p><p> </p><p> </p><p></p><p>\therefore~ cot \theta = \dfrac{1}{2}∴ cotθ= </p><p>2</p><p>1</p><p>$