Question
Simplify each expression using the fundamental identities.
1. Sec x csc x / sec^2x+csc^2x
2. Sec x + tan x / sec x + tan x - cos x
1. Sec x csc x / sec^2x+csc^2x
2. Sec x + tan x / sec x + tan x - cos x
Answers
sin^2+cos^2 = 1, so
sec^2 + csc^2 = 1/cos^2 + 1/sin^2
= (sin^2+cos^2)/(sin^2 cos^2)
= 1/(sin^2 cos^2)
= sec^2 csc^2
so,
(sec csc) / (sec^2 csc^2)
= 1/(sec csc)
= sin cos
= 1/2 sin(2x)
#2 is missing too many parentheses to work on it. That dangling cos x bothers me.
sec^2 + csc^2 = 1/cos^2 + 1/sin^2
= (sin^2+cos^2)/(sin^2 cos^2)
= 1/(sin^2 cos^2)
= sec^2 csc^2
so,
(sec csc) / (sec^2 csc^2)
= 1/(sec csc)
= sin cos
= 1/2 sin(2x)
#2 is missing too many parentheses to work on it. That dangling cos x bothers me.
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