Question

2 math questions please help

Answer 1

Answer:

Step-by-step explanation:

2)Cos²x - Sin² x = √2/2

Cos²x - Sin² x = Cos 2x

⇒ Cos 2x = √2/2

General solution for Cos 2x = √2/2 is

$2x = \dfrac{\pi }{4}+2\pi n \ ; 2x=\dfrac{7\pi }{4}+2\pi n\\\\\\x = \dfrac{\pi }{2*4}+\dfrac{2\pi n }{2} \ ; \ x=\dfrac{7\pi }{4*2}+\dfrac{2\pi n}{2}\\\\\\x =\dfrac{\pi }{8}+\pi n ; \ x=\dfrac{7\pi }{8}+\pi n$

Option A

Answer 2

Answer:

See below for answers and explanations

Step-by-step explanation:

Problem 1

$f(x)=5sin(\frac{x}{12})+14.5\\\\17=5sin(\frac{x}{12})+14.5\\ \\2.5=5sin(\frac{x}{12})\\ \\0.5=sin(\frac{x}{12})\\ \\\frac{x}{12}=\frac{\pi}{6}+2\pi n,\frac{5\pi}{6}+2\pi n\\ \\x=2\pi+24\pi n,10\pi+24\pi n$

Therefore, the fourth option is correct.

Problem 2

$cos^2x-sin^2x=\frac{\sqrt{2}}{2}\\ \\cos(2x)=\frac{\sqrt{2}}{2}\\\\2x=\frac{\pi}{4}+2\pi n,\frac{7\pi}{4}+2\pi n\\ \\x=\frac{\pi}{8}+\pi n,\frac{7\pi}{8}+\pi n$

Therefore, the first option is correct.