Question

If sin x+Cos x =under root 3, then prove tan x +cot x=1

Answer 1

sin x + cos x = √3
Squaring on both sides,
(sin x + cos x)² = √3²
sin²x + cos²x + 2sinx.cosx = 3
1 + 2sinx.cosx = 3
2sinx.cosx = 3-1
sinx.cosx = 2/2
sin x.cos x = 1

»we have to prove: tan x + cot x = 1
LHS = tan x+cot x
= sin x/cos x + cos x/sin x
= sin²x + cos²x/sin x.cos x
= 1/1
= 1
= RHS

Therefore, LHS = RHS
tan x+cos x = 1
Hence proved