Question

sin 30° × cos 30° + sin 60° × cos 30°​

Answer 1

Answer:

Step-by-step explanation:

Q. sin 30 x cos 30 + sin 60 x cos 30

Sol: sin 30 = 1/2

     cos 30 =√3/2

      sin 60 = √3/2

substituting values we get

⇒ 1 x √3       +     √3  x √3

   _____              _______

    2 x 2                  2  x 2

⇒     √3/ 4      + 3/4

⇒(√3 + 3) /4

         

Answer 2

$\huge{\underline{\underline{\mathfrak{\pink{Given\::}}}}}$

• $\bf{sin\:30^{ \circ}}\:\:\:\:\Longrightarrow\:\sf{\dfrac{1}{2}}$

• $\bf{cos\:30^{ \circ}}\:\:\:\:\Longrightarrow\:\sf{\dfrac{\sqrt{3}}{2}}$

• $\bf{sin\:60^{ \circ}}\:\:\:\:\Longrightarrow\:\sf{\dfrac{\sqrt{3}}{2}}$

• $\bf{cos\:30^{ \circ}}\:\:\:\:\Longrightarrow\:\sf{\dfrac{\sqrt{3}}{2}}$

${ }$

$\huge{\underline{\underline{\mathfrak{\pink{To \: Find\::}}}}}$

• $\bf{Their\:Values}$

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$\huge{\underline{\underline{\mathfrak{\pink{Solution\::}}}}}$

• $\sf{sin\:30^{ \circ}\:\times\:cos\:30^{ \circ}\:+\:sin\:60^{ \circ}\:\times\:cos\:30^{ \circ}}$

$\:\:\:\:\:\:\:\::\:\Longrightarrow\:\sf{\dfrac{1}{2}}\:\times\:{\dfrac{\sqrt{3}}{2}}\:+\:{\dfrac{\sqrt{3}}{2}}\:\times\:{\dfrac{\sqrt{3}}{2}}$

$\:\:\:\:\:\:\:\::\:\Longrightarrow\:\sf{\dfrac{\sqrt{3}}{4}}\:+\:{\dfrac{3}{4}}$

$\:\:\:\:\:\:\:\::\:\Longrightarrow\:\sf{\dfrac{\sqrt{{3}}\:+\:3}{4}}$

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$\:\:\:\:\:\:\:\:{\purple{\bold{\dag}}}\:{\underline{\sf{So,\:the\:value\:is\:}\:{\bold{\dfrac{\sqrt{{3}}\:+\:3}{4}}}}}$

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Know More:

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