Question

If sinA+cotA = √2, then evaluate : tanA + cotA.

Answer 1

Heya !!

Given :- sinA + cosA = √2

To find :- tanA + cotA

Proof :- sinA + cosA = √2 (given)

Squaring on both sides

(sinA + cosA)² = (√2)²

=> sin²A + cos²A + 2sinAcosA = 2

=> 1 + 2sinAcosA = 2

=> sinAcosA = 1/2 _(1)

We know that, sin²A + cos²A = 1 _(2)

Dividing _(1) and _(2)

sin²A + cos²A / sinAcosA = 1 ÷ (1/2)

=> sin²A + cos²A / sinAcosA = 2

=> sin²A/sinAcosA + cos²A/sinAcosA = 2

=> sinA/cosA + cosA/sinA = 2

=> tanA + cotA = 2