Question

sin45°cos30 - cos45°sin30°​

Answer 1

Answer:

sin 45°cos30°-cos 45 sin 30

1/ sin45 cos30- cos45 1/sin30

cos45 cos30 -cos 45 cos30

=0

Answer 2

Question:

• sin45°cos30 - cos45°sin30°​

Solution:

$\sf \longmapsto\sin 45^\circ \cos 30^\circ-\cos45^\circ\sin30^\circ\\\\\star\;\textsf{Putting the values}\\\\\mapsto\;\dfrac{1}{\sqrt2}\times \dfrac{\sqrt3}{2}-\dfrac{1}{\sqrt2}\times \dfrac{1}{2}\;\;\;\;\;\;\sf(\red{refer\; to\;table\;provided})\\\\\mapsto\; \dfrac{\sqrt3}{2\sqrt2}-\dfrac{1}{2\sqrt2}\\\\\mapsto\dfrac{\sqrt3-1}{2\sqrt2} \;\\\\\star\textbf{Rationalsing}$

• To rationalise just multiply and divide by the denominator. Here we have denominator 2√2 . so, multiply and divide by it.

$\mapsto\dfrac{\sqrt3-1}{2\sqrt2}\\\\\mapsto \dfrac{\sqrt3-1}{2\sqrt2}\times \dfrac{2\sqrt2}{2\sqrt2}\\\\\mapsto \dfrac{2\sqrt2(\sqrt3-1)}{8}\\\\\mapsto\dfrac{2\sqrt6-2\sqrt2}{8}\\\\\mapsto\dfrac{2(\sqrt6-\sqrt2)}{8}\\\\\mapsto\pink{\dfrac{\sqrt6-\sqrt2}{4}}\\\\\mapsto\dfrac{2.449-1.414}{4}\\\\\mapsto\dfrac{1.035}{4}\\\\\mapsto\pink{ 0.258}$

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Trignometric table :-

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