# ACT Math 3.5 Trigonometry

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ACT Math: Trigonometry Drill 3, Problem 5. Simplify the expression.

ACT Math | Trigonometry |

ACT Mathematics | Trigonometry |

Foreign Language | Arabic Subtitled Chinese Subtitled Korean Subtitled Spanish Subtitled |

Geometry | Right Triangles and Trigonometry |

Language | English Language |

Product Type | ACT Math |

Trigonometry | Solving trigonometric equations Trig identities |

### Transcript

a lot of trig here to simplify this... if you aren't too great with your trig formulas

and identities, we'd recommend you hit pause and review them before you tackle this problem.

formula is just too messy...

formula is just too messy...

So… let's start simplifying it first.

Ok, here goes. First we can separate this nasty thing into two fractions multiplied

by each other

This gives us 2 times sine alpha over cosine alpha times 1 over the quantity 1 minus tangent

squared alpha. Because we know our identities backward and

forward, we know that tangent alpha equals sin alpha over cosine alpha...

...leaving us with 2 times tangent alpha over the quantity 1 minus tangent squared alpha.

But wait - doesn't that look like our formula for tangent 2 alpha?

Why yes, it does. Tangent 2 alpha is our answer. Answer E.