Sin=a/c cos=b/c prove 1+tan=sec

Question

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Answer 1

Well to start with, the problem should be:

 

sin x = a/c

cos x = b/c

Show 1 + tan² x = sec² x

 

tan x = sin x/cos x = (a/c)/(b/c) = a/b

sec x = 1/cosx = 1/(b/c) = c/b

 

1 + tan²x = sec²x

1 + a²/b² = c²/b²

(b² + a²)/b² = c²/b²

 

a² + b² = c²

 

By the Pythagorean Theorem, a² + b² = c², so we have

 

c² = c²

 

Which is always true.