Question

plz give correct ans . Don't give useless answers. ​

Answer 1

Topic :- Basic mathematics

$\maltese\:\underline{\textsf{\textbf{AnsWer :}}}\:\maltese$

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$\longrightarrow\:\:\sf \cos (75^{\circ})$

$\longrightarrow\:\:\sf \cos (45^{\circ} + 30^{\circ})$

$\footnotesize\:\bullet\:\underline{\rm [ \because \: \cos(A + B) = \cos A \cos B - \sin A \sin B ] : }$

$\longrightarrow\:\:\sf \cos 45^{\circ}\cos 30^{\circ} - \sin 45^{\circ}\sin30^{\circ}$

$\longrightarrow\:\:\sf \dfrac{1}{ \sqrt{2} } . \dfrac{ \sqrt{3} }{2} - \dfrac{1}{ \sqrt{2} }. \dfrac{1}{2}$

$\longrightarrow\:\:\sf \dfrac{ \sqrt{3} }{ 2\sqrt{2} } - \dfrac{1}{2 \sqrt{2} }$

$\longrightarrow\:\: \underline{ \underline{\sf \dfrac{ \sqrt{3} - 1}{ 2\sqrt{2} } }}$

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$\longrightarrow\:\:\sf \sin (15^{\circ})$

$\longrightarrow\:\:\sf \sin (45^{\circ} -30^{\circ} )$

$\footnotesize\:\bullet\:\underline{\rm [ \because \: \sin(A - B) = \sin A \cos B - \cos A \sin B ] : }$

$\longrightarrow\:\:\sf \sin 45^{\circ}\cos 30^{\circ} - \cos 45^{\circ}\sin30^{\circ}$

$\longrightarrow\:\:\sf \dfrac{1}{ \sqrt{2} } . \dfrac{ \sqrt{3} }{2} - \dfrac{1}{ \sqrt{2} }. \dfrac{1}{2}$

$\longrightarrow\:\:\sf \dfrac{ \sqrt{3} }{ 2\sqrt{2} } - \dfrac{1}{ 2\sqrt{2} }$

$\longrightarrow\:\: \underline{ \underline{\sf \dfrac{ \sqrt{3} - 1}{ 2\sqrt{2} }}}$

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$\longrightarrow\:\:\sf \sin (75^{\circ})$

$\longrightarrow\: \: \sf\sin(45^{\circ} +30^{\circ} )$

$\footnotesize\:\bullet\:\underline{\rm [ \because \: \sin(A + B) = \sin A \cos B + \cos A \sin B ] : }$

$\longrightarrow\: \: \sf\sin45^{\circ} \cos30^{\circ} + \cos45^{\circ}\sin 30^{\circ}$

$\longrightarrow\:\:\sf \dfrac{1}{ \sqrt{2} } . \dfrac{ \sqrt{3} }{2} + \dfrac{1}{ \sqrt{2} }. \dfrac{1}{2}$

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

$\longrightarrow\:\:\sf \underline{ \underline{\dfrac{ \sqrt{3} + 1}{ 2\sqrt{2} }}}$

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$\longrightarrow\:\:\sf \cos (105^{\circ})$

$\longrightarrow\:\:\sf \cos (60^{\circ} + 45^{\circ})$

$\footnotesize\:\bullet\:\underline{\rm [ \because \: \cos(A + B) = \cos A \cos B - \sin A \sin B ] : }$

$\longrightarrow\:\:\sf \cos 60^{\circ} \cos 45^{\circ} + \sin 60^{\circ} \sin 45^{\circ}$

$\longrightarrow\:\:\sf \dfrac{1}{2} . \dfrac{1}{ \sqrt{2} } - \dfrac{ \sqrt{3} }{2} . \dfrac{1}{ \sqrt{2} }$

$\longrightarrow\:\:\sf \dfrac{1}{2 \sqrt{2} } - \dfrac{ \sqrt{3} }{2 \sqrt{2} }$

$\longrightarrow\:\: \underline{ \underline{\sf \dfrac{1 - \sqrt{3} }{2 \sqrt{2}}} }$

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