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Trigonometry question?

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Prove sec x/sec x + tan x + tan x / sec x- tan x = 1+ 2 tan^2x
asked Nov 5, 2014 in TRIGONOMETRY by anonymous
reshown Nov 5, 2014 by bradely

1 Answer

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Given identity sec x/(sec x + tan x) + tan x / ( sec x- tan x )= 1+ 2 tan^2x

Start from left hand side :

image

Rewrite the expression with common denominator.

image

image

Substitute Trigonometric identity : sec² x - tan² x = 1

image

image

( sec² x - tan² x ) + 2tan²x

Substitute Trigonometric identity : sec² x - tan² x = 1

1 + 2tan²x

Hence Trigonometric identity sec x/(sec x + tan x) + tan x / ( sec x- tan x )= 1+ 2 tan²x is proved.

answered Nov 5, 2014 by lilly Expert

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