Question

If sin A+cosA=√3,then prove that tanA +cotA=1​

Answer 1

as eq.3 =eq.4

we have proved that tanA+cotA=1

Answer 2

Hope it helps you!!!!

LHS = sinA + cosA = √3

RHS = tanA + cot A = 1

Now by first substituting RHS first we get,

sinA /cosA + cosA / sinA = 1

sin^2 + cos^2/ sinAcosA = 1

1/sinAcosA=1

sinAcosA = 1

LHS:

Squaring on both sides:

(sinA + cosA )^2 = (√3)

sin^2A + cos ^2A + 2sinAcosA = 3

1 + 2sinAcosA = 3

2sinAcosA = 3-1

2sinAcosA = 2

sinAcosA = 2/2

sinAcosA = 1

Hence LHS = RHS proved.