Verify each identity:

(tan x + tan y) / (1 - tan x tan y) = (sin x cos y + cos x sin y) / (cos x cos y - sin x sin y)

Question

Mathematics

Dorian Burke

21 December, 15:16

Verify each identity:

(tan x + tan y) / (1 - tan x tan y) = (sin x cos y + cos x sin y) / (cos x cos y - sin x sin y)

+3

Answers (2)

Know the Answer?

Isabella Heath · Answer 1

Using double angle identity in trigonometry, sin x cos y + cos x sin y is equal to the sum of x and y that is the angle inside the sine function notation. On the other hand, cos x cos y - sin x sin y is equal to cos (x+y) while (tan x + tan y) / (1 - tan x tan y) is equal to tan (x+y). Since tan (x+y) = sin (x+y) / cos (x+y), the problem is solved

Sincere Skinner · Answer 2

Tan (x) + tan (y) / 1 - tan (x) tan (y) = sin (x) cos (y) + cos (x) sin (y) / cos (x) cos (y) - sin (x) sin (y)

tan (x + y) = sin (x + y) / cos (x + y)

tan (x + y) = tan (x + y)

Verify each identity:(tan x + tan y) / (1 - tan x tan y) = (sin x cos y + cos x sin y) / (cos x cos y - sin x sin y)

Verify each identity:

(tan x + tan y) / (1 - tan x tan y) = (sin x cos y + cos x sin y) / (cos x cos y - sin x sin y)