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Prove the equations (1.2.3.5) and (1.2.3.7) with the aid of (1.2.3.4) !
(1.2.3.4) |
(1.2.3.5) |
(1.2.3.7) |
In the first equation of (1.2.3.4) by substituting one obtains:
After applying on the result of part 1 :
One obtains from parts 1 and 2:
as required
According to the definition of the tangent function:
The denominator of part 4 can be simplified by substituting in the second equation of (1.2.3.4) and similarly to the result of part 3 , one obtains:
The substitution of the results of parts 3 and 5 into part 4 yields:
But the right-hand side of this equation (part 6) is by definition , therefore the relation (1.2.3.7) was obtained as required.
The exercise does not have to be solved according the above present solution.
The full proof of (1.2.3.5) is worth 4 points. The full proof of (1.2.3.7) is worth 6 points.In the case of incomplete proofs, the points for the different parts are:
The parts 1, 3, 6, 7 are worth one point each. The parts 2, 4, 5 are worth 2 points each.