Question

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

Eᴠᴀʟᴜᴀᴛᴇ :-

I) sɪɴ60°ᴄᴏs30°+sɪɴ30°ᴄᴏs60°
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Answer 1

Evaluate:

I) Sin60° Cos30° + Sin30° Cos60°

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

$Sin60° = \sf\dfrac{\sqrt{3}}{2}$

$Cos30° = \sf\dfrac{\sqrt{3}}{2}$

$Sin30° = \sf\dfrac{1}{2}$

$Cos60° = \sf\dfrac{1}{2}$

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━

$\begin{gathered}\\\end{gathered}$

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

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

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.

Answer 2

Answer:

I) Sin60° Cos30° + Sin30° Cos60°

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━

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

Step-by-step explana

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