Question #f1f92

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Answer 1 · 2017-04-23T20:06:37

See below.

Starting from the LHS.

LHS = #(3 - 4sin^2A)/(cos^2A)#

#= [3 - (3sin^2A + sin^2A)]/(cos^2A)#

#= (3-3sin^2A - sin^2A)/(cos^2A)#

#= (3(1-sin^2A) - sin^2A)/(cos^2A)#

#= (3cos^2A - sin^2A)/(cos^2A)#

#= (3cos^2A)/(cos^2A) - (sin^2A)/(cos^2A)#

#= 3-tan^2A# = RHS

Answer 2 · 2017-04-24T09:36:51

LHS = #(3 - 4sin^2A)/(cos^2A)#

= #3/cos^2A - (4sin^2A)/cos^2A#

= #3sec^2A - 4tan^2A#

= #3(1+tan^2A )- 4tan^2A#

= #3+3tan^2A - 4tan^2A#

= #3 - tan^2A=RHS#