Answer:

[tex] \boxed{ \star \blue{ \large\underline{ \huge \sf \pink{hello \: pooja \: }}}}[/tex]

Given that:-

[tex]\begin{gathered} \\ \: \bf{sɪɴ60°ᴄᴏs30°+sɪɴ30°ᴄᴏs60°} \\ \\ \end{gathered}[/tex]

To find:-

Evaluation

Quick tip:-

Trigonometry values for angles 0°, 30°, 45°, 60°and 90°, with respect to sin, cos, tan, cot, sec, cosec functions, taking an example of the right-angle triangle.

Have a look at the table in the attachment

We know that,

[tex] \sin60 \degree = \frac{ \sqrt{3} }{2} \\ [/tex]

[tex] \cos30 \degree = \frac{ \sqrt{3} }{2} \\ \\ \sin 30\degree = \frac{1}{2} \\ \\ \cos60 \degree = \frac{1}{2} [/tex]

Putting all values

[tex]\begin{gathered} \\ \: \bf{sɪɴ60°ᴄᴏs30°+sɪɴ30°ᴄᴏs60°} \\ \\ \end{gathered}[/tex]

[tex] = ( \frac{ \sqrt{3} }{2} ) \times ( \frac{ \sqrt{3} }{2} ) \times ( \frac{1}{2} ) \times ( \frac{1}{2} )[/tex]

[tex] = \frac{ \sqrt{3} \times \sqrt{3} }{2 \times 2} + \frac{1}{2 \times 2} \\ [/tex]

[tex] = \frac{3}{4} + \frac{1}{4} \\ \\ = \frac{3 \ + 1}{4} \\ \\ = \frac{ \cancel4}{ \cancel4} \\ \\ = 1[/tex]

[tex]\begin{gathered} \\ \: \bf{sɪɴ60°ᴄᴏs30°+sɪɴ30°ᴄᴏs60°} = 1\\ \\ \end{gathered}[/tex]

Hope it helps you from my side!!

Keep Learning!!

[tex] \huge\star \: \rule{200pt}{2.5pt}[/tex]

Verified answer

Given :

• [tex] \sf { Sin 60^{ \circ } Cos 30^{ \circ } + Sin 30^{ \circ } Cos 60^{ \circ } } [/tex]

[tex] \\ \\ [/tex]

To Find :

• Find the Value

[tex] \\ \\ \qquad{\rule{200pt}{2pt}} [/tex]

SolutioN :

[tex] \dag \; {\underline{\underline{\sf{ \; Here \; we \; have \; :- }}}} [/tex]

[tex] \; \; {\longrightarrow \; {\underline{\boxed{\red{\sf{ Sin \; 60^{ \circ } = \dfrac{ \sqrt{3} }{2} }}}}}} \; \; \; \; \; \; \; {\longrightarrow \; {\underline{\boxed{\purple{\sf{ Cos \; 30^{ \circ } = \dfrac{ \sqrt{3} }{2} }}}}}} [/tex]

[tex] \\ [/tex]

[tex] \; \; {\longrightarrow \; {\underline{\boxed{\orange{\sf{ Sin \; 30^{ \circ } = \dfrac{ 1 }{2} }}}}}} \; \; \; \; \; \; \; \; \; {\longrightarrow \; {\underline{\boxed{\green{\sf{ Cos \; 60^{ \circ } = \dfrac{ 1 }{2} }}}}}} [/tex]

[tex] \\ \\ [/tex]

[tex] \dag \; {\underline{\underline{\sf{ \; Calculating \; the \; Value \; :- }}}} [/tex]

[tex] \; \; :\implies \; \sf { Sin 60^{ \circ } Cos 30^{ \circ } + Sin 30^{ \circ } Cos 60^{ \circ } } \\ \\ [/tex]

[tex] \; \; :\implies \; \sf { \bigg\lgroup \dfrac{ \sqrt{3} }{2} \times \dfrac{ \sqrt{3} }{2} \bigg\rgroup + \bigg\lgroup \dfrac{1}{2} \times \dfrac{1}{2} \bigg\rgroup } \\ \\ [/tex]

[tex] \; \; :\implies \; \sf { \dfrac{3}{4} + \dfrac{1}{4} } \\ \\ [/tex]

[tex] \; \; :\implies \; \sf { \dfrac{3 + 1}{4} } \\ \\ [/tex]

[tex] \; \; :\implies \; \sf { \dfrac{4}{4} } \\ \\ [/tex]

[tex] \; \; :\implies \; \sf { \cancel\dfrac{4}{4} } \\ \\ [/tex]

[tex] \; \; :\implies \; {\pmb{\underline{\boxed{\pink{\frak { 1 }}}}}} \; \bigstar \\ \\ [/tex]

[tex] \\ \\ [/tex]

[tex] \qquad \; \therefore \; [/tex] Value of the given Equation is 1

[tex] \\ {\underline{\rule{300pt}{9pt}}} [/tex]

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