Geometry

Sum and Difference Trigonometric Formulas

Sum and Difference Trigonometric Formulas - Problem Solving

         

Which of the following is equal to the above expression?

Rectangle ABCDABCD has side lengths AB=a,BC=24.\overline{AB}=a, \overline{BC}=24. If point PP on BCBC internally divides it 2:12:1 and tan(APD)=3\tan (\angle APD)=3, what is the value of aa?

If sinx=311\sin x=-\frac{3}{11}, the value of 1cotx1+tanx+1+cotx1tanx\frac{1-\cot x}{1+\tan x}+\frac{1+\cot x}{1-\tan x} can be expressed as ab\frac{a}{b}, where aa and bb are corpime positive integers. What is a+ba+b?

If tanθ+cotθ=16\tan \theta + \cot \theta = 16, what is the value of cscθsecθtanθ+cscθsecθ+tanθ\frac{\csc \theta}{\sec \theta - \tan \theta} + \frac{\csc \theta}{\sec \theta + \tan \theta}?

Details and assumptions

Clarification: The function csc, is also known as cosec.

If sinθ+cosθ=16\sin \theta+\cos \theta=\frac{1}{6}, the value of cscθsecθtanθ+cscθsecθ+tanθ\frac{\csc \theta}{\sec \theta-\tan \theta}+\frac{\csc \theta}{\sec \theta+\tan \theta} can be expressed as ab-\frac{a}{b}, where aa and bb are copime positive integers. What is a+ba+b?

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