SOLUTION: prove identity sin x tan x + cos x = sec x

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Question 732932: prove identity
sin x tan x + cos x = sec x
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
sin(x)tan(x) + cos(x) = sec(x)

Use the identity tan%28theta%29=sin%28theta%29%2Fcos%28theta%29

sin(x)·sin%28x%29%2Fcos%28x%29 + cos(x) 

Write the sin(x) as a fraction by putting 1 under it:

sin%28x%29%2F1·sin%28x%29%2Fcos%28x%29 + cos(x)

Multiply the fractions 

sin%5E2%28x%29%2Fcos%28x%29 + cos(x)

Get an LCD of cos(x)

sin%5E2%28x%29%2Fcos%28x%29 + cos(x)·cos%28x%29%2Fcos%28x%29

Write the cos(x) as a fraction by putting 1 under it:

sin%5E2%28x%29%2Fcos%28x%29 + cos%28x%29%2F1·cos%28x%29%2Fcos%28x%29

 Multiply the fractions

sin%5E2%28x%29%2Fcos%28x%29 + cos%5E2%28x%29%2Fcos%28x%29

Combine the numerators over the LCD:

%28sin%5E2%28x%29%2Bcos%5E2%28x%29%29%2Fcos%28x%29

Use the identity sin%5E2%28theta%29%2Bcos%5E2%28theta%29=1

1%2Fcos%28x%29

Use the identity 1%2Fcos%28theta%29=sec%28theta%29

sec(x)

Edwin