Determine an exact value of b such that csc (6b+pi/8)=sec(2b-pi/8)

Question

This is part of the equivalent trigonometric expressions.

 

The answer is: answers may vary. Sample answer:pi/16

 

How do I get this?

Answer 1

Edward,

 

1st, recognize that csc=1/sin and sec=1/cos.  So we can simplify the equation to sin(6b+pi/8)=cos(2b-pi/8).  Generally trig problems are easier if you convert everything to sines and cosines.

 

2nd, sin & cos are 90 degrees out of phase or pi/2 so the cos(x-pi/2)=sin(x)

 

3rd, using (2) we get cos(6b+pi/8-pi/2)=cos(2b-pi/8).

this equation is true if the numbers in parentheses are equal or if one is 2•n•pi larger than the other.

(6b-3pi/8)=(2b-pi/8)->-2pi/8=-4b->pi/16=b