P.T-(cosAcosB+sinAsinB)(cosAcosB-sinAsinB)=cos2^A-sin2^B

Dear Student,

Here the L.H.S. is

(cosAcosB + sinAsinB)(cosAcosB - sinAsinB)

 

= (cosAcosB)² - (sinAsinB)²

= (cos²A)(cos²B) - (sin²A)(sin²B)

 

= cos²A(1 – sin²B) – (1 – cos²A)sin²B  .........{Because sin²A + cos²A = 1}

= cos²A – cos²A sin²B – sin²B  +  cos²Asin²B

= cos²A  – sin²B

= R.H.S

Hence the result is proved

Regards,

Team Topper Learning