Difference between revisions of "1979 AHSME Problems/Problem 20"
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− | == Problem 20 == | + | == Problem #20 == |
If <math>a=\tfrac{1}{2}</math> and <math>(a+1)(b+1)=2</math> then the radian measure of <math>\arctan a + \arctan b</math> equals | If <math>a=\tfrac{1}{2}</math> and <math>(a+1)(b+1)=2</math> then the radian measure of <math>\arctan a + \arctan b</math> equals |
Revision as of 13:08, 8 December 2020
Problem #20
If and
then the radian measure of
equals
SOLUTION
Solution by e_power_pi_times_i
Since ,
. Now we evaluate
and
. Denote
and
such that
. Then
, and simplifying gives
. So
and
. The question asks for
, so we try to find
in terms of
and
. Using the angle addition formula for
, we get that
. Plugging
and
in, we have
. Simplifying,
, so
in radians is
.
See also
1979 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 19 |
Followed by Problem 21 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
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