Question

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

Answer 1

Answer:

LHS :

tan A + Cot A

= Sin A / CosA + Cos A / SinA

= Sin^2 A + Cos^A / Cos A × Sin A ( Taking LCM)

= ( SinA + Cos A )^2 - 2 ( Sin A × Cos A ) / Sin A × Cos A [ ( a + b )^2 - 2ab = a^2 + b^2 ]

= ( Root over 3 )^2 - 2 ( Sin A Cos A ) / Sin A × Cos A

= 3 - 2

= 1

Answer 2

sinA+cosA = √3

squaring both sides

(sinA + cosA)² = 3

1+2sinAcosA = 3

2sinAcosA = 2

sinAcosA = 1

Now

tanA + cotA

=1/sinAcosA

=1/1

=1