Question

What is the exact value of tan(195°)?

Answer 1

It's C

Explanation:

Answer 2

Given:

The value is tan(195°).

To find:

The exact value of tan(195°).

Solution:

We have,

`\tan (195^\circ)=\tan (180^\circ+15^\circ)`

`\tan (195^\circ)=\tan (15^\circ)`
`[\because \tan (180^\circ-\theta)=\tan \theta]`

It can be written as

`\tan (195^\circ)=\tan (45^\circ-30^\circ)`

`\tan (195^\circ)=(\tan (45^\circ)-\tan (30^\circ))/(1+\tan (45^\circ)\tan (30^\circ))`
`[\because \tan (A-B)=(\tan A-\tan B)/(1+\tan A\tan B)]`

`\tan (195^\circ)=(1-(1)/(√(3)))/(1+(1)((1)/(√(3))))`

`\tan (195^\circ)=((√(3)-1)/(√(3)))/(1+(1)/(√(3)))`

`\tan (195^\circ)=((√(3)-1)/(√(3)))/((√(3)+1)/(√(3)))`

`\tan (195^\circ)=(√(3)-1)/(√(3)+1)`

Therefore, the exact value of tan(195°) is
`(√(3)-1)/(√(3)+1)`.