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2 years ago

What is the proof the formula for cos(A+B)=cosAcosB-sinAsinB?

1 answer:

8 0

Given data, cos(A - B) = cosAcosB + sinAsinB
let, A=60' and B=30' ( here the ' sign bears degree) 
L.H.S = cos(A - B) 
=cos (60'-30) ( using value of A and B ) 
=cos30' 
= sqrt3/2 
R.H.S= cosAcosB + sinAsinB 
=cos60' cos30' + sin60' sin30' 
= 1/2* sqrt3/2+ sqrt3/2*1/2 
= sqrt3/4 + sqrt3/4 
=2 sqrt3/4 
= sqrt3/2 
so L.H.S =R.H.S or cos(A - B) = cosAcosB + sinAsinB

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2 years ago

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Answer:

The expression that can be used to determine the final cost of the game is

1.06(0.88 y) ⇒ (C)

Step-by-step explanation:

If the price of an item is discounted, that mean its new price will be less its initial price

The taxes on item, makes its new price greater than the initial price because tax is add

Let us solve the problem

∵ Ella purchased a game that was on sale for 12% off

→ That means the new price will (100% - 12%) of the initial price

∵ y represented the initial price of the game

→ Multiply y by (100% - 12%) to get the new price

∴ The new price = y (100% - 12%)

∴ The new price = y (88%)

→ Change 88% to normal number by divide it by 100

∴ The new price = y ( $\frac{88}{100}$ )

∴ The new price = 0.88 y

∵ The sales tax in her county is 6%

→ That means the final cost will be (100% + 6%) of 0.88 y

∴ The final cost = (100% + 6%) × (0.88 y)

∴ The final cost = 106% × (0.88 y)

→ Change 106% to normal number by divide it by 100

∴ The final cost = $\frac{106}{100}$ × (0.88 y)

∴ The final cost = 1.06(0.88 y)

The expression that can be used to determine the final cost of the game is 1.06(0.88 y)

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2 years ago