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prove trigonometric identities

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secxtanx=cscxcotx
asked Apr 16, 2014 in TRIGONOMETRY by jouis Apprentice

1 Answer

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Sec x tan x = csc x cot x

Left hand side identity = Sec x tan x

=  1 / cos x * ( sin x / cos x

= sin x / cos 2 x

Left hand side identity = sin x / cos 2 x

Right hand side identity = csc x cot x

=  1 / sin x * (cos x / sin x

= cos x / sin 2 x

Right hand side identity = cos x / sin 2 x

Left hand side identity  = Right hand side identity

sin x /cos 2 x  =  cos x / sin 2 x

sin 3 x = cos 3

Let  us assume that  x = π / 4

sin 3 x = sin 3 ( π / 4 ) =  ( 1/ √ 2)3 = 0 . 3535 

cos 3 x = cos 3 (π / 4) = ( 1/ √ 2)3 = 0 . 3535

sin 3 x = cos 3 x

Since period of a sinusoidal function is 2π.

So. it is also true for all x = π / 4 + 2nπ where n is integer.

For all  x values except  x = π / 4 + 2nπ  the identity is not true.

Therefore Sec x tan x ≠ csc x cot x .

answered Apr 17, 2014 by friend Mentor

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