Question

sin 60 ×cos ×30+sin30× cos60

Answer 1

your answer is = 1.☺☺

Answer 2

$\blue{\huge\sf\underbrace{\underline{\underline{Given}} : - - }}$

• Sin 60° × cos 30° + sin 30° × cos60°

$\blue {\huge\sf \overbrace{\underbrace{\underline{\underline{to \: find}} : - - }}}$

• Sin 60° × cos 30° + sin 30° × cos60° =??

$\blue {\huge\sf \overbrace{\underbrace{\underline{\underline{formulas}} : - - }}}$

• $\pmb {\: Sin 60° = \frac{ \sqrt{3} }{2} }$
• $\pmb{ cos 30° = \frac{ \sqrt{3} }{2} }$
• $\pmb{ sin 30° = \frac{1}{2} }$
• $\pmb{cos60° = \frac{1}{2} }$

$\green {\huge\sf \overbrace{\underbrace{\underline{\underline{solution}} : - - }}}$

We know that,

$\sf\longmapsto Sin 60° = \frac{{ \sqrt{3} } }{2} \\ \\ \sf\longmapsto \: cos 30° = \frac{ \sqrt{3} }{2} \\ \\\sf\longmapsto sin 30° = \frac{ {1} }{2} \\ \\\sf\longmapsto cos60° = \frac{1}{2}$

Now we put value in our question

$\rm Sin 60° × cos 30° + sin 30° × cos60° \\ \\ \\ \longmapsto \rm \bigg\lgroup \frac{ \sqrt{3} }{2} \bigg\rgroup \times \bigg\lgroup \frac{ \sqrt{3} }{2} \bigg\rgroup + \bigg\lgroup \frac{1}{2} \bigg\rgroup \times \bigg\lgroup \frac{1}{2} \bigg\rgroup$

Now we open the bracket

$\rm\longmapsto \frac{ \sqrt{3} \times \sqrt{3} }{2 \times 2} + \frac{1 \times 1}{2 \times 2}$

Root are canceled

$\rm\longmapsto \dfrac{ \cancel{\sqrt{3}} \times \cancel{\sqrt{3}} }{2 \times 2} + \dfrac{1 \times 1}{2 \times 2}$

Denominator are multiple

$\longmapsto\rm \dfrac{3}{4} + \dfrac{1}{4} \\ \\ \longmapsto\rm \dfrac{3 + 1}{4} \\ \\ \longmapsto\rm \dfrac{4}{4}$

4 and 4 are canceled

$\longmapsto\rm \cancel\dfrac{4}{4}$

$\large \longmapsto\rm \red1$

Hence, the Sin 60° × cos 30° + sin 30° × cos60° = 1

_________________________

More information

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