Question

2 cos square 60 degree + 3 sec square 30 degree minus 2 tan square 45 degree / sin square 30 degree + cos square 45 degree

Answer 1

Answer:10/3

Step-by-step explanation: By

Answer 2

The value of the expression is $\dfrac{10}{3}$.

Step-by-step explanation:

Consider the provided expression.

$\dfrac{2\cos^2 60+3\sec^2 30-2\tan^2 45}{\sin^2 30+\cos^2 45}$

Use the trivial identity:

$\cos \left(60^{\circ \:}\right)=\frac{1}{2}, \sec \left(30^{\circ \:}\right)=\frac{2}{\sqrt{3}}, \tan \left(45^{\circ \:}\right)=1, \sin \left(30^{\circ \:}\right)=\frac{1}{2}\ and\ \cos \left(45^{\circ \:}\right)=\frac{\sqrt{2}}{2}$

$=\dfrac{2(\dfrac{1}{2} )^2 +3(\dfrac{2}{\sqrt{3}} )^2 -2(1)^2 }{(\dfrac{1}{2})^2+(\dfrac{1}{\sqrt{2}})^2}$

$=\dfrac{\dfrac{1}{2} +4-2 }{\dfrac{1}{4}+\dfrac{1}{2}}$

$=\dfrac{\dfrac{1}{2}+2 }{\dfrac{3}{4}}$

$=\dfrac{5}{2} \times \dfrac{4}{3} =\dfrac{10}{3}$

Hence, the value of the expression is $\dfrac{10}{3}$.

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