How to solve cos(30+60)

Welcome to my article How to solve cos(30+60). This question is taken from the simplification lesson.
The solution of this question has been explained in a very simple way by a well-known teacher by doing addition, subtraction, and fractions.
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First write the question on the page of the notebook.

How to solve cos(30+60)

This question is based on trigonometry,

in this way, to solve this question,

we will also take the help of trigonometry formula

Let us first write this question in this way,

\displaystyle \cos ({{30}^{\circ }}+{{60}^{\circ }})


\displaystyle \cos (A+B)= \displaystyle \cos A\cos B-\sin A\sin B

\displaystyle \cos ({{30}^{\circ }}+{{60}^{\circ }})=\cos {{30}^{\circ }}\cos {{60}^{\circ }}-\sin {{30}^{\circ }}\sin {{60}^{\circ }}

We know that ,


putting the value,

\displaystyle \cos ({{30}^{\circ }}+{{60}^{\circ }})=\frac{{\sqrt{3}}}{2}\times \frac{1}{2}-\frac{1}{2}\times \frac{{\sqrt{3}}}{2}

\displaystyle \cos ({{30}^{\circ }}+{{60}^{\circ }})=\frac{{\sqrt{3}\times 1}}{{2\times 2}}-\frac{{1\times \sqrt{3}}}{{2\times 2}}

\displaystyle \cos ({{30}^{\circ }}+{{60}^{\circ }})=\frac{{\sqrt{3}}}{4}-\frac{{\sqrt{3}}}{4}

\displaystyle \cos ({{30}^{\circ }}+{{60}^{\circ }})=\cancel{{\frac{{\sqrt{3}}}{4}}}-\cancel{{\frac{{\sqrt{3}}}{4}}}

\displaystyle \cos ({{30}^{\circ }}+{{60}^{\circ }})=0


\displaystyle \cos ({{30}^{\circ }}+{{60}^{\circ }})=\cos ({{90}^{\circ }})=0 [Answer]

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