# sin^2 theta + 2 cos theta -1/ (sin^2 theta +3 cos theta-3= cos^2 theta+cos theta/ (-sin^2 theta) Prove the identity

sin^2 theta + 2 cos theta -1/ (sin^2 theta +3 cos theta-3= cos^2 theta+cos theta/
(-sin^2 theta)

Prove the identity.

Start from the left, it would be easy to change sin²(θ) into cos²(θ) using the identity:
sin²(θ)+cos²(θ)=1

Do not forget to put parentheses around the numerator and denominator. The expression that you posted does not evaluate to what you meant.

(sin²(θ)+2cos(θ)-1) / (sin²(θ)+3cos(θ)-3)
=(2cos(θ)-cos²(θ)) /
(3cos(θ)-cos²(θ)-2)
=cos(θ)(2-cos(θ)) / ((cos(θ)-2)(1-cos(θ)))
=cos(θ)/(cos(θ)-1)

multiply by (1+cos(θ)) both numerator and denominator:

= cos(θ)(1+cos(θ)) / ((cos(θ)-1)(1+cos(θ)))
=-cos(θ)(1+cos(θ)) / sin²(θ)
##### Add Answer of: sin^2 theta + 2 cos theta -1/ (sin^2 theta +3 cos theta-3= cos^2 theta+cos theta/ (-sin^2 theta) Prove the identity
Similar Homework Help Questions
• ### prove the identity: sin^2 O/ 1-cos O = 1+cosO O= theta

prove the identity: sin^2 O/ 1-cos O = 1+cosOO= theta

• ### prove the identity : cos^4 theta- sin ^4 thetaover sin squared theta cos squared theta =cot squared theta - tan squared theta

prove the identity : cos^4 theta- sin ^4 thetaover sin squared theta cos squared theta =cot squared theta - tan squared theta

• ### prove the identity cos theta sec theta/cot theta = tan theta

prove the identity cos theta sec theta/cot theta = tan theta

• ### Prove that Sin(theta)times Cos(theta) divided by Cos^2(theta)-Sin^2(theta)=Tan(theta) divided by 1-Tan(theta) Show step by step how to change the left to equal the right side of equasion

Prove that Sin(theta)times Cos(theta) divided by Cos^2(theta)-Sin^2(theta)=Tan(theta) divided by 1-Tan(theta) Show step by step how to change the left to equal the right side of equasion

• ### if cos 2 theta = -(1/3) and theta is in Quadrant 2, find sin theta, cos theta, tan theta, and draw triangle theta

if cos 2 theta = -(1/3) and theta is in Quadrant 2, find sin theta, cos theta, tan theta, and draw triangle theta

• ### Solving for theta? #1/2 = cos^2(2*pi*sin(theta)) #

So apparently I have forgotten all of my undergrad maths, trying to solve the following equation for theta #1/2 = cos^2(2*pi*sin(theta)) # . I know it must be an identity I have forgotten, but I cannot seem to find it online.

• ### prove the following identity cos^4X - sin^4X = 1-2sin^2X

prove the following identitycos^4X - sin^4X = 1-2sin^2X

• ### Sin theta - 2 cos theta sin theta = 0

Sin theta - 2 cos theta sin theta = 0

• ### If cos theta = -sin theta,then sin^2 theta is what

If cos theta = -sin theta,then sin^2 theta is what?

• ### Solve (2+sqrt3)cos theta=1-sin theta?

#(2+sqrt3)cos theta=1-sin theta#

Need Online Homework Help?