Find the value of tan 15 degrees

Exact Value of tan 15° | How to calculate tan15-degree value

Q. Find the value of tan 15 degrees


Let  tan(15°) = tan(45°-30°)

We know that tan(A - B) = (tanA - tanB) /(1 + tan A tan B)

⇒tan(45°-30°) = (tan45°- tan30°)/(1+tan45°tan30°)

= {1- (1/√3)} / {1+(1/√3)}

∴ tan15° = (√3 - 1) / (√3 + 1)

             


            =2−3‾√

Alternate

tan(30o)=tan(2×15o)

⟹13√=2tan(15o)1−tan2(15o)

⟹3‾√=1−tan2(15o)2tan(15o)

⟹tan2(15o)+23‾√tan(15o)−1=0

⟹tan(15o)=−23√±(23√)2−4(1)(−1)√2(1)

=−23√±16√2

=−3‾√±2

So, tan(15o)=2−3‾√ or −(2+3‾√)

As, 15o falls in first quadrant, 
⟹tan(15o)>0

So, tan(15o)=2−3‾√ is the value of tan 15 degree.

After simplification, the value of tan 15 comes out to be 0.26794919243