Question

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

Answer 1

Answer:

Step 1.

SinA+CosA=√3

(SinA+CosA)^2=3

(SinA)^2+(CosA)^2 + 2SinACosA = 3

Since (SinA)^2+(CosA)^2=1

2SinACosA = 2

SinACosA=1

Step 2.

tanA + cotA = 1

SinA/CosA + CosA/SinA = 1

((SinA)^2+(CosA)^2)/SinACosA =1

1/SinACosA =1

SinACosA =1 Same result as Step 1.

Answer 2

sinA+cosA = √3

squaring both sides

(sinA + cosA)² = 3

1+2sinAcosA = 3

2sinAcosA = 2

sinAcosA = 1

Now

tanA + cotA

=sinA/cosA + cosA/sinA

=sin²A+cos²A/sinAcosA

=1/sinAcosA

=1/1

=1