Question

cot ( 90-a) - tan (180-b) ÷ tan (90-a) + cot b

Answer 1

Answer on Question #40518 – Math – Trigonometry

cot (90-a) - tan (180-b) ÷ tan (90-a) + cot b

Solution:

We have to find the result of the expression:

$$cot(90{}^\circ - a) - \frac{\tan(180{}^\circ - b)}{\tan(90{}^\circ - a)} + cot b$$

Formulas for the complementary angles:

$$cot(90{}^\circ - a) = \tan a$$ $$\tan(180{}^\circ - b) = -\tan b$$ $$\tan(90{}^\circ - a) = \cot a$$

(2) and (3) and (4) in (1):

$$\tan a - \left(- \frac{\tan b}{\cot a}\right) + \cot b = \tan a + \tan b \cdot \tan a + \cot b$$

Answer: $\tan a + \tan b \cdot \tan a + \cot b$