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# Sum and Difference Trigonometric Formulas

These formulas explain how to add and subtract trigonometric functions (and their arguments). If you've got sum time, see what a difference these formulas will make for your trig toolkit.

# Sum and Difference Trigonometric Formulas - Problem Solving

Which of the following is equal to the above expression?

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

If $$\sin x=-\frac{3}{11}$$, the value of $\frac{1-\cot x}{1+\tan x}+\frac{1+\cot x}{1-\tan x}$ can be expressed as $$\frac{a}{b}$$, where $$a$$ and $$b$$ are corpime positive integers. What is $$a+b$$?

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

Details and assumptions

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

If $$\sin \theta+\cos \theta=\frac{1}{6}$$, the value of $\frac{\csc \theta}{\sec \theta-\tan \theta}+\frac{\csc \theta}{\sec \theta+\tan \theta}$ can be expressed as $$-\frac{a}{b}$$, where $$a$$ and $$b$$ are corpime positive integers. What is $$a+b$$?

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