Question

2 math questions please help

Answer 1

See below for answers and explanations

Explanation:

Problem 1

`f(x)=5sin((x)/(12))+14.5\\\\17=5sin((x)/(12))+14.5\\ \\2.5=5sin((x)/(12))\\ \\0.5=sin((x)/(12))\\ \\(x)/(12)=(\pi)/(6)+2\pi n,(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=(√(2))/(2)\\ \\cos(2x)=(√(2))/(2)\\\\2x=(\pi)/(4)+2\pi n,(7\pi)/(4)+2\pi n\\ \\x=(\pi)/(8)+\pi n,(7\pi)/(8)+\pi n`

Therefore, the first option is correct.

Answer 2

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 = (\pi )/(4)+2\pi n \ ; 2x=(7\pi )/(4)+2\pi n\\\\\\x = (\pi )/(2*4)+(2\pi n )/(2) \ ; \ x=(7\pi )/(4*2)+(2\pi n)/(2)\\\\\\x =(\pi )/(8)+\pi n ; \ x=(7\pi )/(8)+\pi n`

Option A