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If , , then what is √2 sin x equal to?

This question was previously asked in
CDS Elementary Mathematics 3 Sep 2023 Official Paper
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  1. sin θ + cos θ
  2. sin θ - cos θ

Answer (Detailed Solution Below)

Option 1 : sin θ + cos θ
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Detailed Solution

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Given:

tan x = , 

Formula Used:

1. tan θ = 

2. sin θ =  

3. sin2θ + cos2θ = 1

Calculation:

By Pythagoras Theorem

⇒ H = 

⇒ H = 

⇒ H =  = 

According to the figure

⇒  sin x =  ×  = sinθ + cosθ 

∴ The value of  sin x is equal to sinθ + cosθ.

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