Trigonometric treasure -> 1!

Geometry Level 3

Let $\sec \theta - \tan \theta = 5$ .

If the value of $\cos \theta = \frac AB$ , where $A,B$ are coprime positive integers, submit your answer as $A+B$ .

The answer is 18.

2 solutions

Aryan Sanghi
Jul 9, 2020

$sec^2\theta - tan^2\theta = 1$

$sec\theta + tan\theta = \frac{1}{sec\theta - tan\theta}$

$sec\theta + tan\theta = \frac15$

$sec\theta - tan\theta = 5$

Solving, we get

$sec\theta = \frac{13}{5}$

$cos\theta = \frac{5}{13}$

$\color{#3D99F6}{\boxed{a + b = 5 + 13 = 18}}$

Razing Thunder
Jul 7, 2020

FOR DETAILED SOLUTION

@Razing Thunder @Pi Han Goh @Alak Bhattacharya @Sahil Goyal

After you get your answer, it is a good practice to check your answer. The answer you got corresponds to a 5-12-13 triangle, where the secant minus the tangent is $\frac{1}{5}$ . Although the steps to get to the answer was correct, the final step in the answer where you added the two equations was incorrect, because the answer you got corresponds if you flip the right hand side of the two equations. Thus, there's no answer!

If you want to fix it, change the $5$ in the problem to $\frac{1}{5}$ .

(This question should be reported. There's nothing wrong with getting a report. My questions have been reported too. It's not a bad thing. It shows that we're trying to fix this problem so we can be as accurate as possible.)

Ved Pradhan - 11 months, 1 week ago

can you tell me what i should add in the question to get it correct

Razing Thunder - 11 months, 1 week ago

Change $5$ to $\frac{1}{5}$ .

Ved Pradhan - 11 months, 1 week ago

Trigonometric treasure -> 1!

More from trigonometric series .

The answer is 18.

2 solutions

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