Question

If √3/2 sin60° - 1/2 cosƟ = 1/2, find the angle Ɵ


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Answer 1

Answer:

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Answer 2

Answer:

The angle θ is 60°.

Step-by-step-explanation:

We have given that,

$\displaystyle{\sf\:\dfrac{\sqrt{3}}{2}\:\sin\:60^{\circ}\:-\:\dfrac{1}{2}\:\cos\:\theta\:=\:\dfrac{1}{2}}$

We have to find the angle θ.

Now, we know that,

$\displaystyle{\sf\:\sin\:60^{\circ}\:=\:\dfrac{\sqrt{3}}{2}}$

Now,

$\displaystyle{\sf\:\dfrac{\sqrt{3}}{2}\:\sin\:60^{\circ}\:-\:\dfrac{1}{2}\:\cos\:\theta\:=\:\dfrac{1}{2}}$

$\displaystyle{\implies\sf\:\dfrac{\sqrt{3}}{2}\:\times\:\dfrac{\sqrt{3}}{2}\:-\:\dfrac{1}{2}\:\cos\:\theta\:=\:\dfrac{1}{2}}$

$\displaystyle{\implies\sf\:\dfrac{\sqrt{3}\:\times\:\sqrt{3}}{2\:\times\:2}\:-\:\dfrac{1}{2}\:\cos\:\theta\:=\:\dfrac{1}{2}}$

$\displaystyle{\implies\sf\:\dfrac{3}{4}\:-\:\dfrac{1}{2}\:\cos\:\theta\:=\:\dfrac{1}{2}}$

$\displaystyle{\implies\sf\:\dfrac{1}{2}\:\cos\:\theta\:=\:\dfrac{3}{4}\:-\:\dfrac{1}{2}\:\times\:\dfrac{2}{2}}$

$\displaystyle{\implies\sf\:\dfrac{1}{2}\:\cos\:\theta\:=\:\dfrac{3}{4}\:-\:\dfrac{2}{4}}$

$\displaystyle{\implies\sf\:\dfrac{1}{2}\:\cos\:\theta\:=\:\dfrac{3\:-\:2}{4}}$

$\displaystyle{\implies\sf\:\dfrac{1}{2}\:\cos\:\theta\:=\:\dfrac{1}{4}}$

$\displaystyle{\implies\sf\:\cos\:\theta\:=\:\dfrac{\dfrac{1}{4}}{\dfrac{1}{2}}}$

$\displaystyle{\implies\sf\:\cos\:\theta\:=\:\dfrac{1}{\cancel4}\:\times\:\cancel{2}}$

$\displaystyle{\implies\sf\:\cos\:\theta\:=\:\dfrac{1}{2}}$

We know that,

$\displaystyle{\sf\:\cos\:60^{\circ}\:=\:\dfrac{1}{2}}$

$\displaystyle{\therefore\:\underline{\boxed{\red{\sf\:\theta\:=\:60^{\circ}}}}}$

∴ The angle θ is 60°.