Prove the trigonometric identity (cos(45)tan(45)+sin(45))/(tan(45))=2cos(45)

\frac{\cos\left(45\right)\cdot \tan\left(45\right)+\sin\left(45\right)}{\tan\left(45\right)}=2\cos\left(45\right)

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Answer

$true$

Step by step solution

Problem

$\frac{\cos\left(45\right)\cdot \tan\left(45\right)+\sin\left(45\right)}{\tan\left(45\right)}=2\cos\left(45\right)$
1

Calculating the sine of $45$ degrees

$\frac{0.8509+\tan\left(45\right)\cdot \cos\left(45\right)}{\tan\left(45\right)}=\cos\left(45\right)\cdot 2$
2

Calculating the cosine of $45$ degrees

$\frac{0.8509+\tan\left(45\right)\cdot 0.5253}{\tan\left(45\right)}=0.5253\cdot 2$
3

Multiply $2$ times $\frac{83}{158}$

$\frac{0.8509+\tan\left(45\right)\cdot 0.5253}{\tan\left(45\right)}=1.0506$
4

Calculating the tangent of $45$ degrees

$\frac{0.8509+1.6198\cdot 0.5253}{1.6198}=1.0506$
5

Multiply $\frac{83}{158}$ times $\sqrt[4]{47}$

$\frac{0.8509+0.8509}{1.6198}=1.0506$
6

Add the values $\frac{\sqrt[3]{8}}{2}$ and $\frac{\sqrt[3]{8}}{2}$

$\frac{1.7018}{1.6198}=1.0506$
7

Divide $\sqrt[3]{8}$ by $\sqrt[4]{47}$

$1.0506=1.0506$
8

$1.0506$ equal to $1.0506$

$true$

Answer

$true$

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Problem Analysis

Main topic:

Trigonometric identities

Time to solve it:

0.2 seconds

Views:

148