Question

If cosx=4/5,cscx<0, then sin2x= cos2x= tan2x= ...?

Answer 1

The solution to the problem is as follows:


cscx < 0 means 1/sinx < 0, or sinx < 0. 

sinx = -3/5 because you're dealing with a 3-4-5 triangle, and we established
sinx is negative. 

sin2x = 2sinxcosx = 2*-3/5*4/5 = -24/25 
cos(2x) = cos^2(x) - sin^2(x) = 16/25 - 9/25 = 5/25 = 1/5 

tan2x = sin2x / cos2x = -24/5


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