Question

If 1+cotA = √2 Show that tanA-1=√2

Thanks

Answer 1

1+cotA=√2
or, 1+1/tanA=√2
or, (tanA+1)/tanA=√2
or, tanA+1=√2tanA
or, tanA-√2tanA=-1
or, √2tanA-tanA=1
or, tanA(√2-1)=1
or, tanA=1/(√2-1)
or, tanA=(√2+1)/(√2+1)(√2-1)
or, tanA=(√2+1)/{(√2)²-(1)²}
or, tanA=(√2+1)/(2-1)
or, tanA=√2+1
or, tanA-1=√2 (Proved)