Prove that sin2a cos2b + cos2a sin2b + cos2a cos2b + sin2a sin2b = 1

Dear Student,

Please find below the solution to the asked query:

We have : Sin ² a Cos ² b +  Cos ² a Sin ² b + Cos ² a Cos ² b  + Sin ² a Sin ² b =  1

Taking L.H.S.  :

Sin ² a Cos ² b +  Cos ² a Sin ² b + Cos ² a Cos ² b  + Sin ² a Sin ² b

$\Rightarrow$( Sin ² a Cos ² b + Sin ² a Sin ² b ) +  ( Cos ² a Sin ² b + Cos ² a Cos ² b  )

$\Rightarrow$Sin ² a ( Sin ² b  + Cos ² b ) +  Cos ² a ( Sin ² b  + Cos ² b )

$\Rightarrow$Sin ² a ( 1 ) +  Cos ² a ( 1 )                                               ( We know Sin ² $\mathrm{\theta }$ + Cos ² $\mathrm{\theta }$  = 1 )

$\Rightarrow$Sin ² a  +  Cos ² a

$\Rightarrow$1

Therefore,

L.H.S. =  R.H.S.                                                                            ( Hence proved )

Hope this information will clear your doubts about topic.

If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.

Regards