MATH SOLVE

3 months ago

Q:
# Angle x is such that sin x = a + b and cos x = a − b, where a and b are constants.(i) Show that a^2 + b^2 has a constant value for all values of x.(ii) In the case where tan x = 2, express a in terms of b.

Accepted Solution

A:

Answer:Step-by-step explanation:sin x=a+bcos x=a-bsin²x+cos²x=(a+b)²+(a-b)²=2a²+2b²or 2a²+2b²=1a²+b²=1/2 which is constant for all values of x(ii)[tex]\frac{\sin x}{\cos x}=\frac{a+b}{a-b}\\\tan x=\frac{a+b}{a-b}=2\\a+b=2a-2b\\b+2b=2a-a\\or a=3b[/tex]