Trigonometry Answers

What is the nature of Trigonometry? Practical Application of Trigonometry?

Find the general form of the solutions of the equation x such that sin x = cos 5x

Example: for the equation tanx=1, the solutions can be described by x = pi/4 + n*pi, n is an integer.

Find the general form of the solution of the equation x such that sin x = cos5x. Example: for the equation tan x=1, the solutions can be described by x = pi/4 + n*pi, nEZ

A cone has a slant side measure (m) and a semi-vertical angle 2(x). Prove that the measure r of the radius of the sphere inscribed in the cone is given by:
r = (m sin(4x))/2(1+sin(2x))

Find all values of x for which 2sin(x) = sqrt(4+2sqrt3 cos(x))

I can not do this question, please help. For any triangle ABC, prove that c^2=(a+b)^2[1-k^2cos(1/2)C].

Prove that in any triangle ABC sin1/2(B-C)=((b-c)/a)cos1/2A.

I don't know how to prove that:
2(sin6+cos6)-3(sin4+cos4-1)=0