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# 4.2: Trig Proofs

Difficulty Level: At Grade Created by: CK-12

This activity is intended to supplement Trigonometry, Chapter 3, Lesson 2.

## Problem 1 – Using the Calculator for verification

1. Prove: (1+cosx)(1cosx)=sin2x\begin{align*}(1 + \cos x)(1 - \cos x) = \sin^2x\end{align*}.

Verify the proof graphically. Enter the left side of the equation in Y1\begin{align*}Y_1\end{align*} and the right side of the equation in Y2\begin{align*}Y_2\end{align*}.

## Problem 2 - Confirm your findings

For questions 2 through 5, prove the equation given and then verify it graphically. For cotx\begin{align*}\cot x\end{align*}, type (1tanx)\begin{align*}\left ( \frac{1}{\tan x} \right )\end{align*}. For secx\begin{align*}\sec x\end{align*}, type (1cosx)\begin{align*}\left(\frac{1}{\cos x}\right)\end{align*}.

2. sinxcotxsecx=1\begin{align*}\sin x \cdot \cot x \cdot \sec x = 1\end{align*}

3. sec2x1sec2x=sin2x\begin{align*}\frac{\sec^2 x-1}{\sec^2 x}=\sin^2 x\end{align*}

4. tanx+cotx=secx(cscx)\begin{align*}\tan x + \cot x = \sec x(\csc x)\end{align*}

5. sin2x49sin2x+14sinx+49=sinx7sinx+7\begin{align*}\frac{\sin^2 x-49}{\sin^2 x+14 \sin x+49}=\frac{\sin x-7}{\sin x+7}\end{align*}

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