Trig Identities

0

1718

2

+466

sec 2x = (sec² x)/ (2 - sec² x)

Show that the left side equals the right side.

Shades Mar 21, 2016

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Best Answer

+128599

+10

sec 2x = (sec^2 x)/ (2 - sec^2 x)

1 / cos2x = (sec^2x) / (2 - sec^2x)

Note, Shades....since 5/10 = 1/2 then it is also true that 10/5 = 2/1 .....thus....we can "flip" both fractions and write them as :

cos2x / 1 = (2 - sec^2x) / (sec^2 x)

cos2x = 2/sec^2x - sec^2x/ sec^2x

cos2x = 2/ (1/cos^2x) - 1

cos2x = 2cos^2x - 1 which is an identity

CPhill Mar 21, 2016

2⁺⁰ Answers

+2498

+4

https://www.symbolab.com/solver/step-by-step/sec%202x%20%3D%20%5Cleft%28sec%5E%7B2%7D%20x%5Cright%29%2F%20%5Cleft%282%20-%20sec%5E%7B2%7Dx%5Cright%29/?origin=button

Solveit Mar 21, 2016

+128599

+10

Best Answer

sec 2x = (sec^2 x)/ (2 - sec^2 x)

1 / cos2x = (sec^2x) / (2 - sec^2x)

Note, Shades....since 5/10 = 1/2 then it is also true that 10/5 = 2/1 .....thus....we can "flip" both fractions and write them as :

cos2x / 1 = (2 - sec^2x) / (sec^2 x)

cos2x = 2/sec^2x - sec^2x/ sec^2x

cos2x = 2/ (1/cos^2x) - 1

cos2x = 2cos^2x - 1 which is an identity

CPhill Mar 21, 2016

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