# Trigonometry desperate help, clueless girl here

2. solve cos 2x-3sin x cos 2x=0 for the principal values to two decimal places.

3. solve tan^2 + tan x-1= 0 for the principal values to two decimal places.

4. Prove that tan^2(x) -1 + cos^2(x) = tan^2(x) sin^2 (x).

5.Prove that tan(x) sin(x) + cos(x)= sec(x)

6.Prove that tan(x) cos^2(x)+sin^2(x)= cos(x)+ sin(x)

7.Prove that 1+tan(x)/1-tan(x)= sec^2(x)+ 2tan(x)/1-tan^2(x)

8.Prove that sin^2(x)-cos^2(x)/tan(x)sin(x)+cos(x)tan(x)=cos(x)-con(x)cos(x)

9. find a counterexample to show that the equation sec(x)-cos(x)=sin(x) sec(x) is not an identity

1. #2
cos2x - 3sinx cos2x = 0
(cos2x)(1-3sinx) = 0
as you know, if the product of two numbers is zero, one or the other must be zero. So, cos2x = 0 or 1-3sinx = 0

cos2x=0 means x is pi/4,3pi/4,5pi/4,7pi/4

1-3sinx=0 means x = arcsin(1/3) = .3398
But, you need all angles between 0 and 2pi, so since sinx >0 in Qi and QII,
x = .3398 or pi-.3398=2.8018
******************************
#3.
did this one already also. What was unclear?
*******************************
#4
possibly the most useful trig identity is sin^2 x + cos^2 x = 1. You have

tan^2 x - 1 + cos^2 x
tan^2 x - (1-cos^2 x)
tan^2 x - sin^2 x
*****************************
#5.
tanx sinx + cosx
sinx/cosx * sinx + cosx
(sin^2 x + cos^2 x)/cosx
1/cosx
secx
*****************************
#6.
Must be a typo. If x=pi/4,
tan(x) cos^2(x)+sin^2(x) = 1*1/2 + 1/2 = 1
cos(x)+sin(x) = 1/√2+1/√2 = √2
*****************************
#7.
(1+tanx)/(1-tanx)
(1+tanx)^2 / (1-tan^2 x)
(1 + 2tanx + tan^2 x)/(1-tan^2 x)
(sec^2 x + 2tanx)/(1-tan^2 x)
******************************
#8.
(sin^2 x - cos^2 x)/(tanx*sinx + cosx*tanx)
(sinx-cosx)(sinx+cosx)/(tanx(sinx+cosx))
(sinx-cosx)/tanx
sinx*cotx - cosx*cotx
cosx - cosx*cotx
********************************
#9.
Usually a familiar angle will do the trick. If x=pi/4,
secx-cosx = √2 - 1/√2
sinx*secx = 1/√2*√2 = 1

posted by Steve

First Name

## Similar Questions

1. ### trigonometry

5.Find the complete exact solution of sin x = -√3/2. 10. Solve cos 2x – 3sin x cos 2x = 0 for the principal value(s) to two decimal places. 12. Solve tan^2x + tan x – 1 = 0 for the principal value(s) to two decimal
2. ### trigonometry

5. Find the complete exact solution of sin x = -√3/2. 9. Solve cos 2x – 3sin x cos 2x = 0 for the principal value(s) to two decimal places. 21. Solve tan^2x + tan x – 1 = 0 for the principal value(s) to two decimal
3. ### trig help much appreciated! :))

1. Find the complete exact solution of sin x = . 2. Solve cos 2x – 3sin x cos 2x = 0 for the principal value(s) to two decimal places. 3. Solve tan2 x + tan x – 1 = 0 for the principal value(s) to two decimal places. 4. Prove
4. ### Trigonometry

1.Solve tan^2x + tan x – 1 = 0 for the principal value(s) to two decimal places. 6.Prove that tan y cos^2 y + sin^2y/sin y = cos y + sin y 10.Prove that 1+tanθ/1-tanθ = sec^2θ+2tanθ/1-tan^2θ 17.Prove
5. ### Trigonometry

Solve cos 2x – 3sin x cos 2x = 0 for the principal value(s) to two decimal places. Please explain.
6. ### Trigonometry

Please review and tell me if i did something wrong. Find the following functions correct to five decimal places: a. sin 22degrees 43' b. cos 44degrees 56' c. sin 49degrees 17' d. tan 11degrees 37' e. sin 79degrees 23'30' f. cot
7. ### Trigonometry

Solve tan2 x + tan x – 1 = 0 for the principal value(s) to two decimal places. Please Explain
8. ### precalculus

For each of the following determine whether or not it is an identity and prove your result. a. cos(x)sec(x)-sin^2(x)=cos^2(x) b. tan(x+(pi/4))= (tan(x)+1)/(1-tan(x)) c. (cos(x+y))/(cos(x-y))= (1-tan(x)tan(y))/(1+tan(x)tan(y)) d.
9. ### math

Use the exact values of the sin, cos and tan of pi/3 and pi/6, and the symmetry of the graphs of sin, cos and tan, to find the exact values of si -pi/6, cos 5/3pi and tan 4pi/3. I have found the answers to the first three using
10. ### math

Use the exact values of the sin, cos and tan of pi/3 and pi/6, and the symmetry of the graphs of sin, cos and tan, to find the exact values of sin -pi/6, cos 5/3pi and tan 4pi/3. I have found the answers to the first three using

More Similar Questions