Question

without using calculator find value of tan 75°​

Answer 1

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

Answer 2

tan(A+B)=tanA+tanB1−tanAtanB

tan(75)=tan(45+30)

=tan45+tan301−tan45tan30

=1+13√1−1×13√

=3–√+13–√−1

=(3–√+1)(3–√−1)(3–√+1)(3–√+1)

=2+3–√=3.7320508075

I hope it helps you