SOLUTION: if sec theda = (-13/5) and 90 degrees < theda < 180 degrees , find the exact value of cos2 theda

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Question 1155006: if sec theda = (-13/5) and 90 degrees < theda < 180 degrees , find the exact value of cos2 theda
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

if sec+%28theta%29+=+%28-13%2F5%29 and 90+%3C+theta+%3C+180 degrees ,
find the exact value of cos2 theda (theta)-> not quite sure if you have cos(2theta) or cos%5E2%28theta%29

if you have cos%5E2%28theta%29
use theta in quadrant II [90° to 180°]
if sec+%28theta%29=-13%2F5
cos+%28theta%29=1%2Fsec%28theta%29=-5%2F13
then
cos%5E2+%28theta%29=%28-5%2F13%29%5E2
cos%5E2+%28theta%29=25%2F169


if you have cos%282theta%29=>cos%282theta%29=cos%5E2%28theta%29+-+sin%5E2%28theta%29
and sin%5E2%28theta%29=1-cos%5E2%28theta%29
=>cos%282theta%29=cos%5E2%28theta%29+-+%281-cos%5E2%28theta%29%29
=>cos%282theta%29=2cos%5E2%28theta%29+-+1

cos%282theta%29=%2825%2F169%29+-+1
cos%282theta%29=25%2F169+-+169%2F169
cos%282theta%29=-144%2F169