Question

5cosx -2sin(x/2) +7=0
Help me to find x step by step
pls​

Answer 1

Answer:

x = 180

Step-by-step explanation:

First, you need to know

1. Double-angle formula:

cos(2x) = $cos^{2}x - sin^{2}x$

2. Pythagorean identity:

$cos^{2}x + sin^{2}x = 1$

Back to your problem, replacing the variable by the above:

$5cosx-sin\frac{x}{2}+7 = 0$

$5(cos^{2}\frac{x}{2}-sin^{2}\frac{x}{2}) - 2sin\frac{x}{2} + 7 = 0$ By Double-angle formula

$5(1 - 2sin^{2}\frac{x}{2}) - 2sin\frac{x}{2} + 7 = 0$ By Pythagorean identity

Given $y = \frac{x}{2}$

$5(1-2sin^{2}y) - 2siny + 7 = 0$

$10sin^{2}y+2siny-12=0$

$5sin^{2}y+siny-6=0$

$(5siny + 6)(siny - 1)=0$, we know -1 < sinx < 1, for every x ∈ R

$siny = 1, y =90$

$y = \frac{x}{2}$

$x = 180$