Math, asked by Harshit092004, 10 months ago

If sinθ + cosθ = √2cosθ, (θ ≠ 90°) then the value of tanθ is a) √2 − 1 b) √2 + 1 c) √2 d) −√2

Answers

Answered by hukam0685
25

Answer:

Hence option a) √2-1 is correct.

tanθ= √2-1

Step-by-step explanation:

To find the value of tanθ,

If sinθ + cosθ = √2cosθ, (θ ≠ 90°)

We know that

 tan \theta = \frac{sin \theta}{cos \theta}  \\

To do the same ,divide the LHS and RHS of equation by cos θ

 \frac{sin \theta}{cos \theta}  +  \frac{cos\theta}{cos \theta} =   \sqrt{2} \frac{cos \theta}{cos \theta} \\  \\ tan \theta  +  1 =  \sqrt{2}  \\  \\ tan \theta =  \sqrt{2}  - 1 \\  \\

Hence option a) √2-1 is correct.

Hope it helps you.

Answered by prabhas24480
1

Hence option a) √2-1 is correct.

tanθ= √2-1

Step-by-step explanation:

To find the value of tanθ,

If sinθ + cosθ = √2cosθ, (θ ≠ 90°)

We know that

 tan \theta = \frac{sin \theta}{cos \theta}  \\

To do the same ,divide the LHS and RHS of equation by cos θ

 \frac{sin \theta}{cos \theta}  +  \frac{cos\theta}{cos \theta} =   \sqrt{2} \frac{cos \theta}{cos \theta} \\  \\ tan \theta  +  1 =  \sqrt{2}  \\  \\ tan \theta =  \sqrt{2}  - 1 \\  \\

Hence option a) √2-1 is correct.

Hope it helps you.

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