Question

the value of tan 75 is​

Answer 1

Answer:

(√3+1)(√3-1)

Step-by-step explanation:

the value of tan 75 is (√3+1)(√3-1)

Answer 2

tan(75°) = (√(3) + 1)/(√(3) - 1).


Explanation

tan75 = tan(30+45)

Also, tan(A+B) = (tanA + tanB)/(1 - tanAtanB)

So, tan(30+45) = (tan30+tan45)/(1+tan30tan45)

Now, tan30 = 1/✓3

And, tan45 = 1

Therefore, tan(30+45) = (1/✓3 + 1)/(1+ 1/✓3)

Therefore, tan75 = (1 + 1/✓3)²

So, tan75 = 1 + 1/3 + 2/✓3

So, tan75 = 4/3 + 2/✓3

So, tan75 = (4✓3 + 6)/3✓3

The value of✓3 is 1.73205

So, tan75 = 12.9282/5.19615 = 2.4880344

So, the approximate value of tan75 is 2.4880344