exam Maths Puzzle Numerical Ability

right triangle application problems, a car travels north 53 degrees east for 300 miles. how many miles north and how many miles east has the car traveled?

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The equation represents the formula for total distance traveled. The distance
traveled, d, is equal to the rate of travel, r, multiplied by the time of travel, t. Use thi
I am working on a Proof by Induction and keep getting bogged down in the exponents in the inductive step. Please help me simplify:

5/2[2/3(2^n - 2^(-n))] - 2/3(2^(n-1)- 2^(n-1))