Question

what is the value of tan 45° if sin 45°= 1/√2​

Answer 1

Answer:

tan 45 = 1

Step-by-step explanation:

sin 45 = 1/√2

we know that sin a = 1/ cos a

so, cos 45 = √2

we also know that tan a = sin a/ cos a

so, tan 45 = sin 45 / cos 45

= 1/√2 × √2

= 1

Answer 2

Given,

Value of sin 45° = 1/√2

To find,

Value of tan 45°

Solution,

We can simply solve this mathematical problem by using the following mathematical process.

We know that,

$\tanθ = \frac{ \sinθ }{ \cosθ }$

So,

$\tan45° = \frac{ \sin45°}{\cos45°}$

Now, we know the value of sin 45°. So, we have to calculate the value of cos 45°.

We also know that,

sin θ = cos (90° - θ)

Thus,

sin 45° = cos (90°-45°)

sin 45° = cos 45°

1/√2 = cos 45° [Given that, sin 45° = 1/√2]

So, cos 45° = 1/√2

Finally,

$\tan45° = \frac{ \sin45°}{ \cos45°}$

Or,

$\tan45° = \frac{ \frac{1}{ \sqrt{2} } }{ \frac{1}{ \sqrt{2} } }$

Or,

$\tan45° = \frac{1}{ \sqrt{2} } \times \frac{ \sqrt{2} }{1}$

So, tan 45° = 1

(This will be considered as our final answer.)

Hence, the value of tan 45° is 1