Find sin(2x), cos(2x), and tan(2x) from the given information? csc(x) = 8, tan(x) < 0

1 Answer
Feb 25, 2018

It is given that , #csc(x) = 8#
#=> sinx = 1/cscx = 1/8#

Now, #cos^2x = 1 - sin^2x#
#=> cos^2x = 1- 1/64=63/64#
#=> cosx=(3sqrt7)/8#

  1. #color(red)(sin2x = 2sinxcosx#
    #sin2x= 2xx1/8xx(3sqrt7)/8#
    #sin2x = (3sqrt7)/32#

  2. #color(magenta)(cos2x = 2cos^2x-1#
    #cos2x = (2xx63/64) -1#
    #cos2x = (63/32) -(32/32)#
    #cos2x = (31/32)#

  3. #color(blue)(tan2x = (sin2x)/(cos2x)#
    #tan2x = (3sqrt7)/31#