Geometry

Sum and Difference Trigonometric Formulas

Product to Sum Trigonometric Formulas

         

If a0,sin(x+y)=11a,sin(xy)=2a, a \neq 0, \sin(x+y) = \frac{11}{a}, \sin(x-y) = \frac{2}{a}, what is tanxtany?\displaystyle{\frac{\tan x}{\tan y}}?

If cosα=111\cos \alpha=\frac{1}{11} and cosβ=1011\cos \beta=\frac{10}{11}, the value of sin(α+β)sin(αβ)\sin (\alpha+\beta) \sin (\alpha-\beta) can be expressed as ab\frac{a}{b}, where aa and bb are coprime positive integers. What is the value of a+ba+b?

NN is an integer in the range [0,180] [0, 180] such that

2cos43cos26=cos69+cosN. 2 \cos 43 ^\circ \cos 26 ^\circ = \cos 69 ^ \circ + \cos N ^ \circ.

What is the value of NN?

If a0,sin(x+y)=12a,sin(xy)=5a, a \neq 0, \sin(x+y) = \frac{12}{a}, \sin(x-y) = \frac{5}{a}, what is tanxtany?\displaystyle{\frac{\tan x}{\tan y}}?

Which of the following is equal to cos6θcos2θ? \cos 6 \theta \cos 2 \theta?

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