Question

Which expression has the same value as tan(-45°)?
-tan(45°)
-cot(135°)
-sin(270°)
-cos(180°)

Answer 1

Answer:

I think it's cot(135°)

Step-by-step explanation:

Cot 135° = Cot (π/2 + 45)

and,

Cot (π/2+45)= -tan (45),

because when a trigonometric ratio is impressed by using π/2 the ratio should be changed its opposite like sin value turns into a cos value, tan value turns into cot and vise versa. Then as 135° is in the second sector that means π/2<135°<π. So it should be -tan(45°)

As tan-45°= -tan 45° i think the answer is second one aka cot(135°)

Answer 2

The equivalent expression of tan(-45) is cot(135)

The given trigonometric expression is: tan(-45).

To do this, we make use of the following trigonometry ratio

$\cot (\frac{\pi}{2}+\theta)= -\tan (\theta)$

Substitute 45 for $\theta$.

So, we have:

$\cot (\frac{\pi}{2}+45)= -\tan (45)$

In trigonometry, $\frac{\pi}{2} = 90$.

So, we have:

$\cot (90+45)= -\tan (45)$

Add 90 and 45

$\cot (135)= -\tan (45)$

Also, we have:

$\tan (-45)= -\tan (45)$

So, the equation becomes

$\cot (135)= \tan (-45)$

Rewrite as:

$\tan (-45) = \cot (135)$

Hence, the equivalent expression of tan(-45) is cot(135)

Read more about trigonometry equivalent expressions at:

https://brainly.com/question/4515552