Could someone help me with those two questions. I need to know how to do them without calculator

solve for the interval [0,2pie]

1) cos^2*x-cos2x=0

2) tan(x/2)-sinx=0

1. 👍 0
2. 👎 0
3. 👁 117
1. 1.
cos^sup2;(x)-cos(2x) = 0
(1-sin²(x)) - (cos²(x)-sin²(x)) = 0
(1-sin²(x)) - cos²(x) + sin²(x) = 0
1-cos²(x) = 0
sin²(x) = 0
On the interval [0,2π],
sin²(x) = 0 at x=0, π and 2π

Subsititute x=0, π and 2π into the original equation to check each of the solutions.

2.
a. 2 trivial solutions
By inspection, at x=0 and x=2π,
tan(x/2)=sin(x)=0

b. other solutions
use
tan(x/2)=(1-cos(x))/sin(x), and
1-sin²(x) = cos²(x)
to simplify the expression to:
cos(x)(cos(x)-1)/sin(x) = 0
or cos(x)=0, or cos(x)=1
to give x=π/2, 3π/2, 0, 2π
Check each solution to confirm its validity.

1. 👍 0
2. 👎 0
posted by MathMate

## Similar Questions

1. ### Math(Factorial)

A women student is to answer 10 out of 13 questions on a test. Find the number of choices where she must answer: (a) the first two questions; (b) the first or second questions but not both; (c) exactly 3 out of the first 5

asked by Anonymous on April 9, 2014
2. ### Algebra

A test consist of 15 multiple choice questions, 12 true-false questions and 10 fill in the bland questions. you got 8 questions wrong. what percent of the answers were correct?

asked by Kevin on May 8, 2013
3. ### Criminology/Sociology

My instructor wants me to prepare 15 questions to use to interview a fellow student with so that he can show us how to build a profile on a person based on the answers to the questions. When I asked what type of questions, he said

asked by Lynda on September 14, 2008
4. ### Combination

In a question paper there are two parts A and B . Part A contains 6 questions and part B contains 7 questions . in how many ways a student can select 4 questions in part A of which 2 questions are compulsory and 5 questions in

asked by Venkatesh on March 23, 2016
5. ### overview of teaching techniques

how should students be grouped to best encourage learning? (a)according to same abilities (b)according to same attitudes (c)according to same interests (d)according to a common task (my answer) which of the following types of

asked by susue on August 25, 2011
6. ### Stats

An instructor gives a test with 20 multiple choice questions. There are 4 responses per questions and only one choice correct. The test also has 30 True/False questions. Determine the probability a student randomly guessing on all

asked by Lacey on March 31, 2011
7. ### statistics

You can answer any questions from the questions on an exam. In how many different ways can you choose the questions, assuming that the order in which you choose the questions is irrelevant?

asked by randy on August 6, 2014
8. ### Math

You can answer any 8 questions from the 12 questions on an exam. In how many different ways can you choose the 8 questions, assuming that the order in which you choose the questions is irrelevant?

asked by Rachal on February 10, 2011
9. ### Science

Hi, I have two questions about biology I need help with. 1) Some questions fall outside the realm of science, which of the following questions could not be answered using the scientific method? A)What is the function of the

asked by Jon on September 17, 2011
10. ### Algebra 2

In a quiz program, 3 questions on sprots, 3 questions on general knowledge, and 4 questions on science are printed separately on 10 cards and placed upside down. John is asked to select 2 cards at random. What is the probability

asked by Dena on January 29, 2012
11. ### NVQ level 3 buisness admin

ok im really struggling on the questions on unit 314 hy the hell is there no question marks i have to anwser them like questions,its confusing me?? please can anyone shed a light over my way please.x cheers ema We don't have

asked by emma on June 12, 2006

More Similar Questions