How to solve ecuation: (#sqrt((1-sinx)/(1+sinx))#-#sqrt((1+sinx)/(1-sinx))#)(#sqrt((1-cosx)/(1+cosx)#-#sqrt((1+cosx)/(1-cosx)#=-4 ?

1 Answer
Shwetank Mauria
Jan 8, 2018

#(sqrt((1-sinx)/(1+sinx))-sqrt((1+sinx)/(1-sinx)))(sqrt((1-cosx)/(1+cosx))-sqrt((1+cosx)/(1-cosx)))=4# and not #-4#

Explanation:

#(sqrt((1-sinx)/(1+sinx))-sqrt((1+sinx)/(1-sinx)))(sqrt((1-cosx)/(1+cosx))-sqrt((1+cosx)/(1-cosx)))#

= #(sqrt((1-sinx)^2/(1-sin^2x))-sqrt((1+sinx)^2/(1-sin^2x)))(sqrt((1-cosx)^2/(1-cos^2x))-sqrt((1+cosx)^2/(1-cos^2x)))#

= #((1-sinx)/cosx-(1+sinx)/cosx)((1-cosx)/sinx-(1+cosx)/sinx)#

= #((1-sinx-1-sinx)/cosx)((1-cosx-1-cosx)/sinx)#

= #(-2tanx)xx(-2cotx)#

= #4#

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