Question

write in the simplest form cos[ 2 tan inverse( √1-x/1+x)]​

Answer 1

Please find the attachment

Answer 2

The given question is we have to write the simplest form of

$cos(2{tan}^{ - 1} \frac{ \sqrt{1 - x} }{ \sqrt{1 + x} } )$

In trigonometry sin, cos and tan values are the primary functions there are used while solving an angle problems.

All the trigonometric functions in a trigonometric table are related to the ratios of sides of the triangle and their values can be easily found.

The trigonometric table is a collection of trigonometric ratios

The value of cos can be written in either degree Or radian.

we can simplify the above equation by substituting x= tan theta.

$\cos(2 { \tan }^{ - 1} \frac{ \sqrt{1 - cos \: (theta)} }{ \sqrt{1 + \cos(theta) } } )$

The value of

$1 - cos \: theta = 2 {sin}^{2} \frac{theta}{2} \\ 1 + cos \: theta = 2 {cos}^{2} \frac{theta}{2}$

substituting the above value in the expression we get,

$cos \: (2 {tan}^{ - 1} (tan \frac{theta}{2} ))$

Here the value

${tan}^{ - 1} .tan = \frac{1}{tan} \times tan \: = 1$

so, the above expression becomes

$cos(2 \times \frac{theta}{2} )$

2 and 2 will gets cancelled.

In the final we have

$cos \: (theta) \\ = x$

Hence, the simplified value of the above equation is cos theta.

# spj2

we can find the similar questions through the link given below

https://brainly.in/question/23195985?referrer=searchResults