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CrossFit415
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Homework Statement
sec(a-b) = (cot a cot B+1)/(1+tan a tan B)
so I got 1/cos a (1/cos B) -sin a (sin b) but they got cot a cot B + 1 / 1+tan a tan B
What formula should I use since there's no sec formula?
vela said:If you're trying to verify that the expression is an identity, don't bother. It's not. For a=pi/3 and b=pi/6, for instance, you get sec(a-b)=2/sqrt(3) while the RHS is equal to 1.
eumyang said:I would start with the right-hand side instead, and multiply numerator and denominator by cos A cos B:
[tex]\frac{\sec A \sec B}{1 + \tan A \tan B} \cdot \frac{\cos A \cos B}{\cos A \cos B} = ...[/tex]
Can you take it from there?
The equation is a trigonometric identity that relates the secant of the difference of two angles, a and B, to the cotangent and tangent functions of those angles.
This equation can be used in various fields of science, such as physics, engineering, and astronomy, to solve problems involving angles and trigonometric functions.
Yes, this equation can be derived from the Pythagorean identities and the sum and difference identities for sine and cosine.
Yes, this equation can be rewritten as "Sec(a-B) = (cosB+sinB)/(cosB-sinB)", which is a form that is often easier to work with in calculations.
Yes, this equation can be used in navigation, surveying, and geology to calculate distances and angles between objects or locations.