Question

Value of sin60cos30 + sin30 cos60 is​

Answer 1

Answer in the attachment............

hope attachment will helps

Answer 2

${\tt{\red{\underline{\underline{\huge{Answer= \: 1}}}}}}$

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$\LARGE{\bf{\underline{\underline\color{purple}{Solution:-}}}}$

$\boxed{ \sf \blue{ We \: know \: that \: }}$

• $\sf\green{ \sin(60°) \: = \: \frac{ \sqrt{3} }{2} }$

• $\sf\green{ \cos(30°) \: = \: \frac{ \sqrt{3} }{2} }$

• $\sf\green{ \sin(30°) \: = \: \frac{ 1 }{2} }$

• $\sf\green{ \cos(60°) \: = \: \frac{ 1 }{2} }$

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$\boxed{ \sf \red{ Putting \: all \: the \: Values }}$

$\begin{gathered}\begin{gathered}: \implies \underline{ \boxed{\displaystyle \sf \bold{\: sin60°\: cos30° \: + \: sin30°\: cos60° }} }\\ \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}: \implies \displaystyle \sf \: \binom{ \sqrt{3} }{2} \: \times \: \binom{ \sqrt{3} }{2} \: + \: \binom{1}{2} \: \times \: \binom{1}{2} \\ \\ \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}: \implies \displaystyle \sf \: \frac{ \sqrt{3} \: + \: \sqrt{3} }{2 \: \times \: 2} \: + \: \frac{1}{2 \: \times \: 2} \\ \\ \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}: \implies \displaystyle \sf \: \frac{3}{4} \: + \: \frac{1}{4} \\ \\ \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}: \implies \displaystyle \sf \: \frac{3\: + \: 1}{4} \: \\ \\ \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}: \implies \displaystyle \sf \: \frac{ 4}{4} \: \\ \\ \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}: \implies \underline{ \boxed{\displaystyle \sf \bold{\: 1 }} }\\ \\\end{gathered}\end{gathered}$

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$\boxed{ \sf \red{ Hence,\: the \: value \: of \: sin60° cos30 \: + \: sin30 cos60 \: = \: 1}}$

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More about t-ratio

$\boxed{ \sf \green{ T - Ratios}}$

$\begin{gathered}\begin{gathered}\boxed{\boxed{\begin{array}{ |c |c|c|c|c|c|} \bf\angle A & \bf{0}^{ \circ} & \bf{30}^{ \circ} & \bf{45}^{ \circ} & \bf{60}^{ \circ} & \bf{90}^{ \circ} \\ \\ \rm sin A & 0 & \dfrac{1}{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3} }{2} &1 \\ \\ \rm cos \: A & 1 & \dfrac{ \sqrt{3} }{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{1}{2} &0 \\ \\ \rm tan A & 0 & \dfrac{1}{ \sqrt{3} }& 1 & \sqrt{3} & \rm Not \: De fined \\ \\ \rm cosec A & \rm Not \: De fined & 2& \sqrt{2} & \dfrac{2}{ \sqrt{3} } &1 \\ \\ \rm sec A & 1 & \dfrac{2}{ \sqrt{3} }& \sqrt{2} & 2 & \rm Not \: De fined \\ \\ \rm cot A & \rm Not \: De fined & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } & 0 \end{array}}}\end{gathered}\end{gathered}$

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