Cos^2B-sin^2A/(sin A cos A + sin B cos B) = cot (A + B)​

Step-by-step explanation:

Compound angle formula:

sin(A + B)=sinAcosB+cosAsinB

cos(A - B)=cosAcosB+sinAsinB

nominator:

(cos^2B-sin^2A)

=cos^2B-(cos^2B)(sin^2A)-sin^2A+(cos^2B)(sin^2A)

=(cos^2B)(1-sin^2A)-(sin^2A)(1-cos^2B)

=(cos^2B)(cos^2A)-(sin^2A)(sin^2B)

=[(cosB)(cosA)]^2-[(sinA)(sinB)]^2

=(cosAcosB-sinAsinB)(cosAcosB+sinAsinB)

=cos(A + B)cos(A - B)

denominator:

(sin A cos A + sin B cos B)=sin(A + B) cos(A - B)

cos^2B-sin^2A/(sin A cos A + sin B cos B)

=[cos(A + B)cos(A - B)] / [sin(A + B) cos(A - B)]

=cos(A + B)/sin(A + B)

=1/tan(A+B)

=cot(A+B)

answer: 42

use a calculator to find that 845/73 = 11.575

the whole part of the answer is 11. multiply this by 73 to get 11*73 = 803.

subtract that result from 845 to get 845 - 803 = 42

let y equal to

the total fare and x is the mile of taxi ride. so the equation is

y = 0.55x + 1.75

since susie has

$10 to spend for a taxi cab, so he can have

10 = 0.55x +

1.75

x = 15 miles of

taxi ride

so the system of

inequality is

10 < 0.55x +

1.75

x > 2