SOLUTION: i need help solving for tan theta + cot theta is equal to sec theta over sin theta

Question 736672: i need help solving for tan theta + cot theta is equal to sec theta over sin theta
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
tan theta + cot theta is equal to sec theta over sin theta
------------
tan + cot = sec/sin
tan + 1/tan = 1/(sin*cos)
(tan^2 + 1)/tan = 1/(sin*cos)
sec^2/tan = 1/(sin*cos)
sec^2*cos/sin = 1/(sin*cos)
Multiply by sin
sec^2*cos = 1/sin
sec = 1/sin
1/cos = 1/sin
cos = sin
cos^2 = sin^2 = 1 - cos^2
2cos^2 = 1
cos^2 = 1/2
cos = sqrt(2)/2
-------------
theta = pi/4, 3pi/4
------------------
Those are the principal values.
You can add or subtract 2pi*n to/from them, n = 1, 2, 3...

RELATED QUESTIONS
Please help me :) Find theta for 0 degrees less tha or equal to ( (answered by gonzo)
Please help me solve for sin(theta) 1. cot(theta)=-1/5, (theta) is in quadrant IV 2.... (answered by stanbon)
How to solve the following: sin theta cot^2 theta sec ^2 theta = ? Answers: a)sec... (answered by lwsshak3)
establish each identity A) sec^4 theta - sec^2 theta = tan^4 theta + tan^2 theta (answered by solver91311)
FOR THE ACUTE ANGLE sin theta =3/5, FIND: COS theta TAN theta COT theta SEC theta... (answered by ikleyn,MathTherapy)
1.Given: cos theta = 5/13, theta is in quadrand I. Find:tan theta. 2.Given:sin... (answered by Theo)
help the step by step process for this. establish the identity of sec theta over tan... (answered by jsmallt9)
given angle theta is in the 1st quadrant,and tan theta equals 5/12, find sin theta cos... (answered by lwsshak3)
A point P is on the terminal side of angle theta. Evaluate the six trigonometric... (answered by stanbon)