Hey guys! Does anybody know the answer to tan2x-2cosx=0

If the equation is tan(2x) - 2 cos(x) = 0:

We have

tan(2x) = sin(2x) / cos(2x)

sin(2x) = 2 sin(x) cos(x)

So, rewriting the equation gives

tan(2x) - 2 cos(x) = 0

2 sin(x) cos(x) / cos(2x) - 2 cos(x) cos(2x) / cos(2x)= 0

2 cos(x) • (sin(x) - cos(2x)) / cos(2x) = 0

The left side is 0 whenever the numerator is 0:

2 cos(x) = 0   or   sin(x) - cos(2x) = 0

cos(x) = 0   or   sin(x) - (1 - 2 sin²(x)) = 0

cos(x) = 0   or   2 sin²(x) + sin(x) - 1 = 0

cos(x) = 0   or   (2 sin(x) - 1) (sin(x) + 1) = 0

cos(x) = 0   or   2 sin(x) - 1 = 0   or   sin(x) + 1 = 0

cos(x) = 0   or   sin(x) = 1/2   or   sin(x) = -1

Solving each case gives 3 families of solutions:

[x = π/2 + 2nπ   or   x = -π/2 + 2nπ]   or

[x = π/6 + 2nπ   or   x = 5π/6 + 2nπ]   or

[x = -π/2 + 2nπ]

where n is any integer. The last family is already accounted for in the first, so

x = π/2 + 2nπ   or   x = -π/2 + 2nπ   or   x = π/6 + 2nπ   or   x = 5π/6 + 2nπ

the population of other specie of birds will decline or other specie of birds will find some alternate source of food to survive.

explanation:

according to the competitive exclusion principle, which is also known as gause's law, two specie living in the same niche and feeding on the same resource cannot co-exist stably.

as we have well studied the theory of natural selection which states that only those organisms survive which have better tendency to compete for food and adapt to the environmental conditions.

coming towards the question, what wi ll happen when one species outcompetes the other for the small fish , the other specie will not get enough food and will start to die or decline in population. eventually either other specie needs to find another alternative food source for itself or migrate at some other location where there is less competition otherwise it will just not exist anymore at that niche.

hope it !

answer: 5100 just subtract

step-by-step explanation: