Q.Find the value of tanπ/8. ?
suppose x=π/8
➡️2x= π/4
We know, tan2x= 2tanx/1-tan²x
➡️tanπ/4= 2tanπ/8 /1-tan²π/8
➡️ 1= 2tanπ/8 /1-tan²π/8. {tanπ4=1}
➡️1-tan²π/8=2tanπ/8
➡️-tan²π/8-2tanπ/8+1=0
➡️tan²π/8+2tanπ/8-1=0
➡️sec²π/8-1+2tanπ/8-1=0. {tan²π8=sec²π8-1}
,➡️sec²π/8+2tanπ/8-2=0
➡️sec²π/8+2tanπ/8=2
➡️1+tan²π/8+2tanπ/8=2. {sec²π8=1+tan²π8}
➡️tan²π/8+2tanπ/8+1=2
➡️tan²π/8+tanπ/8+tanπ/8+1=2
➡️tanπ/8(tanπ/8+1) +1(tanπ/8+1)=2
➡️(tanπ/8+1)(tanπ/8+1)=2
➡️(tanπ/8+1)²=2
➡️tanπ/8+1=√2
➡️tanπ/8=√2-1
So, tanπ/8=√2-1
because π/8 is in first quadrant, therfore, tanπ/8 is always positive.
stupidity 