Question

5. tan2 A cos2 A = 1 - cos2 A.​

Answer 1

Answer:

ANSWER

LHS = tan

2

θcos

2

θ

=

cos

2

θ

sin

2

θ

×cos

2

θ

=sin

2

θ

=1−cos

2

θ

=RHS

Answer 2

   1 - cos2x = (cos2x)(tan2x)

Recall the following identities:

     sin2x + cos2x = 1     ==>     sin2x = 1 - cos2x

     tan x = sin x/cos x     ==>     tan2x = sin2x/cos2x

Thus,

     1 - cos2x = (cos2x)(tan2x)

        sin2x   = (cos2x)(sin2x/cos2x)

        sin2x   = (cos2x·sin2x)/cos2x

        sin2x   = (cos2x/cos2x)·sin2x

        sin2x   = (1)sin2x

        sin2x   =   sin2x