Prove:
tan 70° = tan 20° + 2tan 50°

As we all know,
According to the trigonometric identity,
tan70=tan(20+50)
tan70=(tan20+tan50)/1-tan20tan50
tan70-tan20tan50tan70=tan20+tan50
Also tan70tan20=tan70cot70=1
Hence
tan70-tan50=tan20+tan50
So tan70=tan20+2tan50
Hope this helps :) :)

tan(70-20)=tan50
 tan70-tan20/1+tan20 tan70=tan50
 tan20 tan70=cot70 tan70=1
 tan70-tan20/2=tan50
 tan70-tan20=2tan50
 tan70=tan20+2tan50

9514 1404 393

  136

Step-by-step explanation:

The attached chart shows the result of using the numbers in the problem statement to calculate the percentage of the population in each category.

95% accuracy on infected individuals is assumed to mean that 95% of the 2% who are infected return a positive test result. The other 5% return a negative test result.

Similarly, 90% accuracy on uninfected individuals is assumed to mean that 90% of the 98% who are not infected will return a negative test result, and the remaining 10% of those 98% will return a (false) positive test result.

Then of the 11.7% who return a positive test result, only 1.9% are actually infected. This fraction is a/b = 19/117, so ...

  a + b = 19 + 117 = 136

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Additional comment

When forming ratios of percentages, one must be very clear about the base of the percentage. Above, the base for every percentage is the entire population of mathletes. The fraction 19/117 is the fraction of those who tested positive that are actually infected (about 16.2% of positives).