Question

Hᴇʏ ɢᴜʏs,

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

Mɪss Aᴄᴄɪᴅᴇɴᴛᴀʟ ɢᴇɴɪᴜs࿐​

Answer 1

Answer :-

• Sin60° Cos30° + Sin30° Cos60° = 1.

Explanation :-

Here, we have to find out the value of this expression.

We know that,

• Sin60° = $\sf\dfrac{ \sqrt{3} }{2}$

• Cos30° = $\sf\dfrac{ \sqrt{3} }{2}$

• Sin30° = $\sf\dfrac{1}{2}$

• Cos60° = $\sf\dfrac{1}{2}$

So, Just Substitute the values.

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

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

$\implies\sf{\dfrac{3}{4} + \dfrac{1}{4} }$

$\implies\sf{ \dfrac{3 + 1}{4} }$

$\implies\sf{ \dfrac{4}{4} }$

$\implies\tt\red{1}.$

Therefore,

Sin60° Cos30° + Sin30° Cos60° = 1.

Extra Information :-

Some Basic Trigonometry Formulas,

• sin θ = Opposite Side/Hypotenuse.
• cos θ = Adjacent Side/Hypotenuse.
• tan θ = Opposite Side/Adjacent Side.
• sec θ = Hypotenuse/Adjacent Side.
• cosec θ = Hypotenuse/Opposite Side.
• cot θ = Adjacent Side/Opposite Side.

Reciprocal Identities,

• cosec θ = 1/sin θ.
• sec θ = 1/cos θ.
• cot θ = 1/tan θ.
• sin θ = 1/cosec θ.
• cos θ = 1/sec θ.
• tan θ = 1/cot θ.