Tanx= sinx/cosx. therefore, tan(90-a)= . (all angle measurements are in degrees.) 1/tan(90-a) 1/sin a 1/cos(90-a) 1/tan a

tan(90 - A) = 1/tan(A) ⇒ last answer

Step-by-step explanation:

* Lets revise some important information for the right triangle

- In any right triangle

# The side opposite to the right angle is called the hypotenuse

# The other two sides are called the legs of the right angle

* If the name of the triangle is ABC, where B is the right angle

∴ The hypotenuse is AC

∴ AB and BC are the legs of the right angle

- ∠A and ∠C are two acute angles

∵ The sum of the interior angles of any triangle is 180°

∵ m∠B = 90°

∴ m∠A + m∠C = 180° - 90° = 90°

- If the measure of angle A is x°

∴ The measure of angle C = 90° - x°

- tan(A) = opposite/adjacent

∵ The opposite to ∠A is BC

∵ The adjacent to ∠A is AB

∴ tan(A) = BC/AB  ⇒(1)

- tan(C) = opposite/adjacent

∵ The opposite to ∠C is AB

∵ The adjacent to ∠C is BC

∴ tan(C) = AB/BC ⇒  (2)

- From (1) and (2)

∴ tan(A) = 1/tan(C)

∵ m∠A = A , m∠C = (90 - A)

∴ tan(A) = 1/tan(90 - A)

OR

∴ tan(90 - A) = 1/tan(A)

LAST OPTION.

Step-by-step explanation:

Remember that:

Then, you need to rewrite :

Applying the identities, you get:

Finally, you must simplify. Then: