Question

sin theta +cos theta =✓2 then find theta​

Answer 1

Answer:

θ = 45 degrees or pi/4 radians

Step-by-step explanation:

sin θ + cos θ = √2

=> (sin  θ  + cos  θ )² = 2                          [squaring both sides]

=> sin² θ + cos² θ + 2 sin θ * cos θ = 2

=> 1 + 2 sin θ * cos θ = 2                          [sin² θ + cos² θ = 1]

=> 2 sin θ * cos θ = 1

=>  sin θ * cos θ = 1 / 2

=>  sin θ * cos θ =  1/√2 * 1/√2

comparing

sin θ =  1/√2   and cos θ = 1/√2

sin θ =  sin 45   and cos θ = cos 45  [ sin 45 = 1/√2 and cos 45 = 1/√2]

Hence θ = 45 degrees or pi/4 radians

Answer 2

Answer:

theta =45°

Step-by-step explanation:

sin45°+cos45°

=

$\frac{1}{ \sqrt{2} } + \frac{1}{ \sqrt{2 } } = \frac{ 2 }{ \sqrt{2} }$

$2 = \sqrt{2} \times \sqrt{2}$

$\frac{ \sqrt{2} \times \sqrt{2} }{ \sqrt{2} }$

$\sqrt{2}$

so answer is 45°