Question

Cos60sin30 + sin60cos30

Answer 1

Answer:

1

Step-by-step explanation:

1/2 x 1/2 + ✓3/2 x ✓3/2

1/4 + 3/4

4/4 = 1.

Answer 2

$\large\underline{\sf{Solution-}}$

Given Trigonometric expression is

$\rm :\longmapsto\:cos60 \degree \: sin30 \degree \: + \: sin60 \degree \: cos30 \degree$

We know, from Trigonometric table of some standard angles, we have

$\purple{\rm :\longmapsto\:cos60 \degree = \dfrac{1}{2}}$

$\purple{\rm :\longmapsto\:cos30 \degree = \dfrac{ \sqrt{3} }{2}}$

$\purple{\rm :\longmapsto\:sin60 \degree = \dfrac{ \sqrt{3} }{2}}$

$\purple{\rm :\longmapsto\:sin30 \degree = \dfrac{1}{2}}$

So, on substituting the values in given expression, we get

$\rm \:  =  \: \dfrac{1}{2} \times \dfrac{1}{2} + \dfrac{ \sqrt{3} }{2} \times \dfrac{ \sqrt{3} }{2}$

$\rm \:  =  \: \dfrac{1}{4} + \dfrac{3}{4}$

$\rm \:  =  \: \dfrac{1 + 3}{4}$

$\rm \:  =  \: \dfrac{4}{4}$

$\rm \:  =  \: 1$

Hence,

$\rm\implies \:\boxed{\tt{ cos60 \degree \: sin30 \degree \: + \: sin60 \degree \: cos30 \degree = 1}}$

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$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\sf Trigonometry\: Table \\ \begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\boxed{\begin{array}{ |c |c|c|c|c|c|} \bf\angle A & \bf{0}^{ \circ} & \bf{30}^{ \circ} & \bf{45}^{ \circ} & \bf{60}^{ \circ} & \bf{90}^{ \circ} \\ \\ \rm sin A & 0 & \dfrac{1}{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} &1 \\ \\ \rm cos \: A & 1 & \dfrac{ \sqrt{3} }{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{1}{2} &0 \\ \\ \rm tan A & 0 & \dfrac{1}{ \sqrt{3} }&1 & \sqrt{3} & \rm \infty \\ \\ \rm cosec A & \rm \infty & 2& \sqrt{2} & \dfrac{2}{ \sqrt{3} } &1 \\ \\ \rm sec A & 1 & \dfrac{2}{ \sqrt{3} }& \sqrt{2} & 2 & \rm \infty \\ \\ \rm cot A & \rm \infty & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } & 0\end{array}}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$