Inactive Tutor answered • 08/14/15
Tutor
New to Wyzant
a) we know that sin2x + cos2x = 1 and cos 2x = cos2x - sin2x
therefore,
1+cos2x = (sin2x + cos2x) +(cos2x - sin2x)
= 2cos2x
b) as csc[(PIE/2)-x] = sec x and sec2x = 1+ tan2x
Therefore,
csc2[(PIE/2)-x]-1 = sec2x - 1
= 1 + tan2x - 1
= tan2x
Inactive Tutor
csc[(PIE/2)-x] = sec x because of complementary angle property which says csc(Π/2 -θ) = secθ
so csc2[(PIE/2)-x] = sec2 x
and csc2[(PIE/2)-x] -1 = sec2-1
= (1+ tan2x ) -1 ; as we know that there is an identity sec2x = 1+ tan2x
= tan2x
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08/14/15
Amber M.
Thank You!
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08/14/15
Amber M.
08/14/15