Question

If sin theta + cos theta =root3 then prove that tan theta + cot theta =1​

Answer 1

sin theta + cos theta = 1

squaring on both sides

=> (sin theta + cos theta)²= (√3)²

=> sin² theta + cos²theta + 2sin theta cos theta = 3

=> 1+ 2sin theta cos theta = 3

=> 2sin theta cos theta = 3-1 = 2

=> sin theta cos theta = 1......(1)

we have to prove that

tan theta + cot theta = 1

LHS

$\frac{sin \: theta}{cos \: theta} + \frac{cos \: theta}{sin \: theta} \\ = \frac{ {sin}^{2}theta + {cos}^{2} theta}{sin \: theta \: cos \: theta} \\ = \frac{1}{sin \: theta \: cos \: theta} \\ = 1 \\ because \: sin \: theta \: cos \: theta \: = 1 \: from \: (1)$