Question

Hᴇʏ ɢᴜʏs,
$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\sf Trigonometry\: Table \\ \begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\boxed{\begin{array}{ |c |c|c|c|c|c|} \bf\angle A & \bf{0}^{ \circ} & \bf{30}^{ \circ} & \bf{45}^{ \circ} & \bf{60}^{ \circ} & \bf{90}^{ \circ} \\ \\ \rm sin A & 0 & \dfrac{1}{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} &1 \\ \\ \rm cos \: A & 1 & \dfrac{ \sqrt{3} }{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{1}{2} &0 \\ \\ \rm tan A & 0 & \dfrac{1}{ \sqrt{3} }&1 & \sqrt{3} & \rm \infty \\ \\ \rm cosec A & \rm \infty & 2& \sqrt{2} & \dfrac{2}{ \sqrt{3} } &1 \\ \\ \rm sec A & 1 & \dfrac{2}{ \sqrt{3} }& \sqrt{2} & 2 & \rm \infty \\ \\ \rm cot A & \rm \infty & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } & 0 \end{array}}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}$
TrigonometryTable
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Qᴜᴇsᴛɪᴏɴ-:
Eᴠᴀʟᴜᴀᴛᴇ ᴛʜɪs :
I) sɪɴ60°ᴄᴏs30°+sɪɴ30°ᴄᴏs60°
Yᴏᴜ ᴄᴀɴ ᴛᴀᴋᴇ ʜᴇʟᴘ ғʀᴏᴍ ᴛʜᴇ ᴀʙᴏᴠᴇ ᴛᴀʙʟᴇ.

Mɪss Aᴄᴄɪᴅᴇɴᴛᴀʟ ɢᴇɴɪᴜs࿐



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Answer 1

Evaluate:

I) Sin60° Cos30° + Sin30° Cos60°

⠀⠀⠀⠀$\dag\;{\underline{\frak{As\;we\;know\;that, \ the \ Trigonometric \ Values\: :}}}$

• Sin60° = $\sf\dfrac{\sqrt{3}}{2}$

• Cos30° = $\sf\dfrac{\sqrt{3}}{2}$

• Sin30° = $\sf\dfrac{1}{2}$

• Cos60° = $\sf\dfrac{1}{2}$

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━

$\dag\;{\underline{\frak{Substituting \ all \ Values \ :}}}$

$:\implies\Bigg(\sf \dfrac{\sqrt{3}}{2} \Bigg) \Bigg(\dfrac{\sqrt{3}}{2}\Bigg) + \Bigg(\dfrac{1}{2}\Bigg) \Bigg(\dfrac{1}{2}\Bigg) \\\\\\:\implies\sf \dfrac{(\sqrt{3}) (\sqrt{3})}{2 \times 2} + \dfrac{1}{2 \times 2} \\\\\\:\implies\sf \dfrac{3}{4} + \dfrac{1}{4} \\\\\\:\implies\sf \cancel\dfrac{4}{4}\\\\\\:\implies{\underline{\boxed{\frak{\pink{\:1\:}}}}}$

Answer 2

Answer:

SoluTion :-

According to given table

$\tt \: \sin60 \degree = \dfrac{ \sqrt{3} }{2}$

$\tt \: \cos \: 30 \degree = \dfrac{ \sqrt{3} }{2}$

$\tt \: \sin30 \degree = \dfrac{1}{2}$

$\tt \cos \: 30 \degree \: = \dfrac{1}{2}$

Putting Values

$\big( \dfrac{ \sqrt{3} }{2} \big)\big( \dfrac{ \sqrt{3} }{2} \big) + \big(\dfrac{1}{2} )\big(\dfrac{1}{2} )$

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

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

$\huge \bf \: = 1$