Question

Can you please solve it with explanation​

Answer 1

Correct Question:-

If sin θ + cos θ = (√2) (cos θ) , (θ ≠ 90°) then the value of tan θ is :

A) √2 - 1

B) √2 + 1

C) √2

D) - √2

Answer:-

Method - 1:

Given:

sin θ + cos θ = (√2) cos θ

Transposing cos θ to RHS we get,

⟶ sin θ = √2 cos θ - cos θ

⟶ sin θ = cos θ (√2 - 1)

⟶ sin θ/cos θ = √2 - 1

using tan θ = sin θ/cos θ we get,

⟶ tan θ = √2 - 1

___________________________

Method - 2:-

sin θ + cos θ = (√2)(cos θ)

Dividing both sides with by cos θ we get,

⟶ (sin θ + cos θ) / cos θ = (√2)(cos θ) / cos θ

⟶ sin θ/cos θ + cos θ/cos θ = √2

⟶ tan θ + 1 = √2

⟶ tan θ = √2 - 1

∴ Required answer is (√2 - 1) [ Option - A ].

Answer 2

$tan = \frac{sin}{cos} \\ tan = \frac{sin}{sin + cos} \\ tan = \frac{sin}{sin} + \frac{sin}{tan} \\ tan = 1 + \frac{sin}{cos} \\ so \: the \: answer \: must \: be \: 1 + \sqrt{2} . \\ hope \: it \: helps$