Question

cot^2x+tan^2x=2 solve equation​

Answer 1

Answer:

x = 45°

Step-by-step explanation:

cot²x + tan²x = 2

cot²x + (1/cot²x) = 2

.............. (•.• 1/cot²x =tan²x)

cot^4x + 1 = 2cot²x

cot^4x - 2cot²x + 1 = 0

cot^4x - cot²x - cot²x + 1 = 0

cot²x (cot²x - 1 ) - 1(cot²x - 1) = 0

(cot²x - 1) (cot²x - 1) = 0

(cot²x - 1)² = 0

taking square root on both the sides

cot²x - 1 = 0

cot²x = 1

cotx = √1

cotx = 1

we know, cot 45° = 1

therefore cotx = 1 , x = 45°