Question

Find theta, if Tan theta = √3+1/√3-1

Answer 1

Step-by-step explanation:

tan theta = √3+1/√3-1

(√3+1)^2 + (√3-1)^2 = hyp^2

hyp = 2√2

sin theta = √3+1/2√2

cos theta = √3-1/2√2

theta =90-15

= 75°

Answer 2

θ is 5π/12 or 75°

Given

tanθ = (√3+1)/(√3-1)

To Find

The value of θ

Solution

$tan\theta = \frac{\sqrt{3} + 1}{\sqrt{3}-1}$

We know that

√3 = tan60°

1 = tan45°

therefore

$tan\theta = \frac{tan60^o + tan45^o}{tan60^otan45^o-1}$                                                       [1]

now, tan(a + b)= (tana + tanb)/(1 - tanatanb)

Therefore, conferring eq [1] to the above formula we get,

$tan\theta = -\frac{tan60^o + tan45^o}{1-tan60^otan45^o}$

$or, tan\theta = - tan (60^o + 45^o)$

$or, tan\theta = - tan (105^o)$

Converting this into radians we get

105°= 105/180 X π

= 7π/12

Using this we get

$tan\theta = - tan (7\pi /12)$

$or, tan\theta = - tan (\pi - 5\pi /12)$

As we can see that this falls in the second quadrant. Since the tan function is negative in the second quadrant we will get,

$tan\theta = tan ( 5\pi /12)$

or, tanθ = 5π/12

= 75°

Therefore θ is 5π/12 or 75°

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