Question

prove thar( tan 60-tan 45)/(1+tan 60*tan45)​

Answer 1

Answer:

I hope this will help you

Answer 2

Given,

( tan 60-tan 45)/(1+tan 60*tan45)​ is given.

To find,

We have to find the value of ( tan 60-tan 45)/(1+tan 60*tan45)​.

Solution,

The value of ( tan 60-tan 45)/(1+tan 60*tan45)​ is (2 - √3).

We can simply find the value of ( tan 60-tan 45)/(1+tan 60*tan45)​ by using the concepts of trigonometry.

As we know,

tan60° = √3, tan45° = 1

  =( tan 60-tan 45)/(1+tan 60*tan45)​

Using the values of tan60° and tan 45°, we get

 = (√3-1)/ (1+√3 * 1)

 = (√3-1) / (√3 + 1)

Since we noted that root is present in the denominator, so to remove root from the denominator, we will rationalize the denominator.

= √3 - 1 / √3 + 1 * √3-1/√3-1

Using (a-b)(a-b) = (a-b)² and (a+b)(a-b) = a²-b², we get

= (√3-1)² / (√3)² - (1)²

=  (√3)² +(1)² - 2√3 /2

= 4 - 2√3/2

Taking 2 common, we get

= 2(2 - √3)/2

= (2 - √3)

Hence, the value of ( tan 60-tan 45)/(1+tan 60*tan45)​ is (2 - √3).