Question

Evaluation sin30 cos45+cos30 sin45

Answer 1

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                                         -Jai

Answer 2

To evaluate

$\sf \bigstar \:sin \: 30 \degree \: cos \: 45 \degree + cos \: 30 \degree \: sin \: 45 \degree$

Solution:-

$\sf \bigstar \:sin \: 30 \degree \: cos \: 45 \degree + cos \: 30 \degree \: sin \: 45 \degree$

sin 30° = 1/2

cos 45° = 1/√2

cos 30° = √3/2

sin 45° = 1/√2

Put all values,

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

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

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

Therefore,

$\sf \bigstar \:sin \: 30 \degree \: cos \: 45 \degree + cos \: 30 \degree \: sin \: 45 \degree = \dfrac{ \sqrt{3} + 1}{2 \sqrt{2} }$