MATH SOLVE

2 months ago

Q:
# 5cosx -2sin(x/2) +7=0Help me to find x step by steppls

Accepted Solution

A:

Answer:x = 180Step-by-step explanation:First, you need to know 1. Double-angle formula:cos(2x) = [tex]cos^{2}x - sin^{2}x[/tex]2. Pythagorean identity:[tex]cos^{2}x + sin^{2}x = 1[/tex]Back to your problem, replacing the variable by the above:[tex]5cosx-sin\frac{x}{2}+7 = 0[/tex][tex]5(cos^{2}\frac{x}{2}-sin^{2}\frac{x}{2}) - 2sin\frac{x}{2} + 7 = 0[/tex] By Double-angle formula[tex]5(1 - 2sin^{2}\frac{x}{2}) - 2sin\frac{x}{2} + 7 = 0[/tex] By Pythagorean identityGiven [tex]y = \frac{x}{2}[/tex][tex]5(1-2sin^{2}y) - 2siny + 7 = 0[/tex][tex]10sin^{2}y+2siny-12=0[/tex][tex]5sin^{2}y+siny-6=0[/tex][tex](5siny + 6)(siny - 1)=0[/tex], we know -1 < sinx < 1, for every x ∈ R[tex]siny = 1, y =90 [/tex][tex]y = \frac{x}{2}[/tex][tex]x = 180[/tex]