Someone please help me

 see proof below

Step-by-step explanation:

Use the Double Angle Identity:  cos 2A = 2cos²A - 1

Use the Difference Identity:  cos (A - B) = cosA · cosB + sinA · sinB

Use the Unit Circle to evaluate:  cos (π/2) = 0   &     sin (π/2) = 1

Proof  LHS → RHS

LHS = RHS:   sin A = sin A  

Below.

Step-by-step explanation:

Left side = 2 cos^2 ( π/4 - A/2) - 1

= 2 ( cos π/4  cos A/2 + sin π/4  sin A/2)^2 - 1

Now sin π/4 and cos π/4 = 1 /√2 so:

= 2 ( 1/√2 cos A/2 + 1/√2 sin A/2)^2 - 1

= 2  * 1/2( cos^2 A/2 + sin^2 A/2 + 2 sin A/2 cos A/2) - 1

But cos^2 a/2 + sin^2 A/2 = 1 so we have:

2 * 1/2( 1 +  2sin A/2 cos A/2) - 1

= 1  + 2 sin A/2 cos A/2 - 1

=  2 sin A/2 cos A/2

Using the identity 2 sin A cos A = sin 2A

2 sin A/2 cos A/2 = sin A  = right side.

So left side = right side and the identity is proved.

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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rauschg

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