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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: $(1 + \cos x)(1 - \cos x) = \sin^2x$.

Verify the proof graphically. Enter the left side of the equation in $Y_1$ and the right side of the equation in $Y_2$.

## Problem 2 - Confirm your findings

For questions 2 through 5, prove the equation given and then verify it graphically. For $\cot x$, type $\left ( \frac{1}{\tan x} \right )$. For $\sec x$, type $\left(\frac{1}{\cos x}\right)$.

2. $\sin x \cdot \cot x \cdot \sec x = 1$

3. $\frac{\sec^2 x-1}{\sec^2 x}=\sin^2 x$

4. $\tan x + \cot x = \sec x(\csc x)$

5. $\frac{\sin^2 x-49}{\sin^2 x+14 \sin x+49}=\frac{\sin x-7}{\sin x+7}$

Feb 23, 2012

Nov 04, 2014