If cosq = – 1/2 and θ lies in third quadrant, then

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If cosq = – 1/2 and θ lies in third quadrant, then what will be the value of sinθ + tanθ

1. 1
  2
2. 2
  √3
3. √3
  2
4. 1
  √3

Correct Option: C

Here, cosθ = – 1/2 and θ, lies in third quadrant

Consider ∆ABC,
Using Pythagoras theorem,
AC² = AB² + BC²
2² = (–1)² + BC²
⇒ BC² = 4 – 1
BC² = 3
BC = √3

tanθ + sinθ = –		√3		+ -			√3
		- 1					2

∵ In third quadrant sinθ is negative and tanθ is positive.
=

=	√3
	2