Question

if sin theeta+cos theeta=root 2 the evaluate tantheeta +cot theeta

Answer 1

Hello
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Given that : - sinθ + cosθ = √2

To find : - value of tanθ + cotθ = ?

Now,

sinθ + cosθ = √2

On squaring both sides,

(sinθ + cosθ)² = (√2)²

=> sin²θ + cos²θ + 2sinθcosθ = 2

=> 1 + 2sinθcosθ = 2

=> 2sinθcosθ = 2 - 1

=> sinθcosθ = ½ .......(i)

Now,

tanθ + cosθ

= sinθ/cosθ + cosθ/sinθ

= (sin²θ + cos²θ) / sinθcosθ

= 1 / sinθcosθ

= 1 / ½ [From (i)]

= 2

HOPE IT HELPS

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ArchitectSethRollins