RTP: [a tan(u) + b]² + [b tan(u) - a]² = (a² + b²) sec²(u)
Proving LHS = RHS:
LHS = [a tan(u) + b]² + [b tan(u) - a]²
= a² tan²(u) + 2ab tan(u) + b² + b² tan²(u) - 2ab tan(u) + a²
= (a² + b²) tan²(u) + (a² + b²)
= (a² + b²)[tan²(u) + 1]
= (a² + b²) sec²(u), using the identity: tan²(x) + 1 = sec²(x)
= RHS
Answer:
The simplified expression to the given expression is 
Therefore 
Step-by-step explanation:
Given fractional expression is 
To simplify the given expression as below :


( using the property
)
![=\frac{2[(2)^4(x^{12})(y^{16})]}{(2)^3(x^6)(y^{18})}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B2%5B%282%29%5E4%28x%5E%7B12%7D%29%28y%5E%7B16%7D%29%5D%7D%7B%282%29%5E3%28x%5E6%29%28y%5E%7B18%7D%29%7D)
( ( using the property
)
( using the property
)
![=2[2^1x^6y^{-2}]](https://tex.z-dn.net/?f=%3D2%5B2%5E1x%5E6y%5E%7B-2%7D%5D)
( using the property
)
Therefore the simplified expression is 
Therefore 
Answer:
36
Step-by-step explanation:
6^ +6-1-5=36
Complete question :
You have decided to stop drinking Starbucks coffee and invest that money in an IRA. If you deposit $492 each month earning 6% interest, how much will you have in the account after 40 years?
Answer:
$250,329.60
Step-by-step explanation:
Given:
Principal, P= $492 per month
= $492 * 12 = $5,904 per year
Rate, R= 6%
Time, T= 40 years
Let's first find the amount after 40 years.
Amount = 5940 * 40 = $236,160
The interest after 40 years =

Interest = $14,169.60
The total amount I will have in my account after 40 years:
Amount + interest
= $236,160 + $14,169.60
= $250,329.60