Question

5 sin square 30 + cos square 45 - 4 x square 30 / 2 sin 30 into cos 30 + tan 45 find the value

Answer 1

Answer: 5/6(√3+2)

Step-by-step explanation: given below

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Answer 2

The required value of the expression is $\frac{5\left(2-\sqrt{3}\right)}{6}$.

Step-by-step explanation:

Consider the provided information.

$\frac{\left(5sin^230+cos^245-4tan^230\right)}{2sin30\:cos30+tan45}$

Use the trivial identity:

$\sin \left(30^{\circ \:}\right)=\frac{1}{2}, \cos \left(45^{\circ \:}\right)=\frac{\sqrt{2}}{2}, \tan \left(30^{\circ \:}\right)=\frac{\sqrt{3}}{3}, \cos \left(30^{\circ \:}\right)=\frac{\sqrt{3}}{2}\ and\ \tan \left(45^{\circ \:}\right)=1$

$\frac{5\sin ^2\left(30^{\circ \:}\right)+\cos ^2\left(45^{\circ \:}\right)-4\tan ^2\left(30^{\circ \:}\right)}{2\sin \left(30^{\circ \:}\right)\cos \left(30^{\circ \:}\right)+\tan \left(45^{\circ \:}\right)}=\frac{5\left(\frac{1}{2}\right)^2+\left(\frac{\sqrt{2}}{2}\right)^2-4\left(\frac{\sqrt{3}}{3}\right)^2}{2\cdot \frac{1}{2}\cdot \frac{\sqrt{3}}{2}+1}$

$=\frac{\frac{5}{4}+\frac{1}{2}-\frac{4}{3}}{\frac{\sqrt{3}}{2}+1}\\\\=\frac{\frac{5}{12}}{\frac{\sqrt{3}+2}{2}}\\\\=\frac{10}{12\left(2+\sqrt{3}\right)}\\\\=\frac{5}{6\left(2+\sqrt{3}\right)}$

Rationalize the denominator.

$=\frac{5\left(2-\sqrt{3}\right)}{6\left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right)}\\\\=\frac{5\left(2-\sqrt{3}\right)}{6}$

Hence, the required value of the expression is $\frac{5\left(2-\sqrt{3}\right)}{6}$.

#Learn more

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