Question

Value of Theta Question Maths
Please Answer​

Answer 1

Answer:

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Answer 2

Answer:

Step-by-step explanation:

We have,

$\tt{cos(\theta)+\sqrt{3}\,sin(\theta)=2}$

$\tt{\implies\,\dfrac{1}{2}cos(\theta)+\dfrac{\sqrt{3}}{2}\,sin(\theta)=1}$

$\tt{\implies\,sin\left(\dfrac{\pi}{6}\right)cos(\theta)+cos\left(\dfrac{\pi}{6}\right)sin(\theta)=1}$

$\tt{\implies\,sin(\theta)\,cos\left(\dfrac{\pi}{6}\right)+cos(\theta)\,sin\left(\dfrac{\pi}{6}\right)=1}$

$\tt{\implies\,sin\left(\theta+\dfrac{\pi}{6}\right)=1}$

$\tt{\implies\,sin\left(\theta+\dfrac{\pi}{6}\right)=sin\left(\dfrac{\pi}{2}\right)}$

$\tt{\implies\,\theta+\dfrac{\pi}{6}=(4n+1)\dfrac{\pi}{2}}$

$\tt{\implies\,\theta=(4n+1)\dfrac{\pi}{2}-\dfrac{\pi}{6}\,\,\,\,\,\,\forall\,n\in\mathbb{Z}}$