Trigonometric Equation: Solving tan(\alpha)=\sqrt{2}-1 for \alpha in ]0,90°[

[mtayab1994]

Homework Statement

tan(\alpha)=\sqrt{2}-1 for every alpha in ]0,90°[

Homework Equations

1-count tan(2α)

2-conclude the value of α

The Attempt at a Solution

1-after using tan(2α)=(2tanα)/1-tan^2α) i got tan(2α)=(√2-1)/2

2- I know that α is pi/8 but i just don't know how to conclude it.

 

[LCKurtz]

Homework Statement

tan(\alpha)=\sqrt{2}-1 for every alpha in ]0,90°[

Homework Equations

1-count tan(2α)

2-conclude the value of α

The Attempt at a Solution

1-after using tan(2α)=(2tanα)/1-tan^2α) i got tan(2α)=(√2-1)/2

2- I know that α is pi/8 but i just don't know how to conclude it.

Write that as$$\frac {\sqrt 2 - 1}{1}$$Then divide the numerator and denominator by $\sqrt 2$ and see if you recognize the result in form$$
\frac{1-\cos\theta}{\sin\theta}$$ for some $\theta$, and see if that formula rings any bells.

 

[Mark44]

Homework Statement

tan(\alpha)=\sqrt{2}-1 for every alpha in ]0,90°[

The above should say, "for alpha in ]0,90°[".

Homework Equations

1-count tan(2α)

2-conclude the value of α

The Attempt at a Solution

1-after using tan(2α)=(2tanα)/1-tan^2α) i got tan(2α)=(√2-1)/2

Your value for tan(2α) is incorrect. Show us how you got that value, and we'll help you get the right value.

2- I know that α is pi/8 but i just don't know how to conclude it.

 

[mtayab1994]

Write that as$$\frac {\sqrt 2 - 1}{1}$$Then divide the numerator and denominator by $\sqrt 2$ and see if you recognize the result in form$$
\frac{1-\cos\theta}{\sin\theta}$$ for some $\theta$, and see if that formula rings any bells.

if i write it like you said and i keep solving, it just brings me back to tanα=√2-1

 

[LCKurtz]

Write that as$$\frac {\sqrt 2 - 1}{1}$$Then divide the numerator and denominator by $\sqrt 2$ and see if you recognize the result in form$$
\frac{1-\cos\theta}{\sin\theta}$$ for some $\theta$, and see if that formula rings any bells.

if i write it like you said and i keep solving, it just brings me back to tanα=√2-1

Show me what you did when you wrote it that way. What $\theta$ works?

 

[Mark44]

It's much simpler if you follow their hint.

1-count tan(2α)

I assume this means compute tan(2α). If you do this, you get a very simple value for tan(2α), which you can use to find α.

 

[mtayab1994]

yea i solved it tan(2α)=1 and to conclude the value of α i did tan(2σ)=tanpi/4+2kpi and i just solve it out and i get α=pi/8