Question

If sin B + cos B = $\sqrt{3}$ ,
THEN PROVE THAT :- tan B + cot B = 1

Answer 1

Answer:

SinB + CosB =√3 (given)

Squaring on both sides :

Sin²B + Cos²B + 2.SinB.CosB = 3

1 + 2SinB.CosB = 3

(as Sin²B + Cos²B =1)

2.SinB.CosB = 2

SinB.CosB = 1 .... (1)

TanB = SinB/ CosB

CotB = CosB/ SinB

TanB + CotB = (sinB/cosB) +(cosB+sinB)

==> (sin²B + cos²B) /(sinB.cosB)

==> 1/sinB.cosB

===1/1 [from (1)]

Hence proved