Question

cos theta = √2 find theta​

Answer 1

Answer:

Given, cosθ+sinθ=2–√

Also, cosθ=2–√−sinθ ……. (i)

Now, we solve cosθ+sinθ=2–√,

Squaring both sides,

(cosθ+sinθ)2=(2–√)2

cos2θ+sin2θ+2cosθsinθ=2

1+2cosθsinθ=2 [Since, sin2θ+cos2θ=1]

1+2⋅(2–√−sinθ)⋅sinθ=2 [From (i)]

1+22–√sinθ−2sin2θ=2

Re-arranging the equation,

2sin2θ−22–√sinθ+1=0

(2–√sinθ)2−2⋅2–√sinθ⋅1+(1)2=0

(2–√sinθ−1)2=0

Square rooting both sides,

2–√sinθ−1=0

2–√sinθ=1

sinθ=12√

sinθ=sin45° [Since, sin45°=12√]

Eliminating sin from both sides

θ=45°