Question

Given
sinA +cosA =√3
prove that
tanA+cotA=1​

Answer 1

Step-by-step explanation:

given,sinA +cosA=√3

divide the equation by cos A-

tanA + 1 = √3cosA

tanA=√3cosA-1 (name this as eqn 1)

Now divide the equation by sinA-

1+cotA = √3sinA

cotA=√3sinA-1 (name this as eqn 2)

Now add eqn1 & eqn2 ,we get-

tanA + cotA = (√3cosA-1 )+ (√3sinA-1)

tanA + cotA=√3cosA+√3sinA-2

tanA + cotA=√3(cosA+sinA)-2

tanA + cotA=(√3*√3)-2

tanA + cotA=3-2

tanA + cotA=1. Hence proved.

I hope this helps☺️