Question

if sin theta=cos theta,where 0⁰is greater then theta greater then 90⁰, then tan theta+cot theta=
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Answer 1

Answer:

Sinθ + Cosθ > 1  if θ is an acute angle

Step-by-step explanation:

From the above question,

Cot 60° = 1/√3

Cos60° = 1/2

Therefore ,

(Cot 60° - cos 60°)/(cot60° + cos60°)

= ( 1/√3 - 1/2)/(1/√3 + 1/2)

Let say

Sinθ + Cosθ  = x

As θ is an acute angle so Sinθ & Cosθ are positive

so x is also positive

Squaring both  sides

=> (Sinθ + Cosθ)²  = x²

=> Sin²θ + Cos²θ + 2SinθCosθ = x²

Using Sin²θ + Cos²θ = 1  & Sin2θ = 2SinθCosθ

=> 1 + Sin2θ = x²

as θ is an acute angle so 2θ will lie either in 1st Quadrant or 2nd quadrant

0°<θ<90° => 0°<2θ<180° =>

=> Sin2θ is + ve  

=> 1 + (+ve)  = x²

=> x² > 1

=> x > 1

=> Sinθ + Cosθ > 1

= ( 2-√3)/(2+√3)

For more related question : https://brainly.in/question/28467835

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