Question

Sin A + cosA=√3, then prove tan A + cot A=1

Answer 1

Answer:

Given - sin θ + cos θ = √3

To Prove - tan θ + cot θ =1

Property - sin2 θ + cos2 θ = 1

Answer Given equation –

sin θ + cos θ = √3

squaring on both sides,

∴ (sin θ + cos θ)2 = 3

∴ sin2 θ + cos2 θ + 2sin θ. cos θ = 3

∴ 1 + 2sin θ. cos θ = 3 ………( sin2 θ + cos2 θ = 1)

∴ 2sin θ. cos θ = 2

∴ sin θ. cos θ = 1 ………(1)

Now,

L.H.S. = tan θ + cot θ

………from (1)

= 1

= R.H.S.

∴ L.H.S. = R.H.S.

Hence Proved !!!

Answer 2

Answer:

hope this help you mate..