I have to prove:
(1-sin^2xcsc^2x +sin^2x)/cos^2x = tan^2x
Every time I solve it i get it equal to tan^2x + 1
Could someone help me, any help would be appreciated thanks!
(1-sin^2xcsc^2x +sin^2x)/cos^2x = tan^2x
Every time I solve it i get it equal to tan^2x + 1
Could someone help me, any help would be appreciated thanks!
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Well the csc^2(x) can be made to be 1/sin^2(x), so then you will have sin^2(x)[1/(sin^2(x))] and those cancel out to give you 1.
So now you have 1-1+sin^2(x)/[cos^2(x)]. The ones cancel each other out.
And then sin^2(x)/cos^2(x)= tan^2(x)
So now you have 1-1+sin^2(x)/[cos^2(x)]. The ones cancel each other out.
And then sin^2(x)/cos^2(x)= tan^2(x)
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working from the left hand side
(1-sin^2x*csc^2x+sin^2x)/cos^2x =
(1-1+sin^2x)/cos^2x =
sin^2x/cos^2x = tan^2x
the key here is that csc^2x = 1/sin^2x, so sin^2x * csc^2x = 1
(1-sin^2x*csc^2x+sin^2x)/cos^2x =
(1-1+sin^2x)/cos^2x =
sin^2x/cos^2x = tan^2x
the key here is that csc^2x = 1/sin^2x, so sin^2x * csc^2x = 1