How to simplify (cosA.cosB)^2-(sinA.sinB)^2 ?

Answer 1

Hi Mohammed, to simplify cosA^2 * cosB^2 - sinA^2 * sinB^2

You can make use of the trig identity:

cosX^2 + sinX^2 = 1

Then you have:

(1-sinA^2) * (1-sinB^2) - sinA^2 * sinB^2

=1 - sinB^2 - sinA^2 + sinA^2 * sinB^2 - sinA^2 * sinB^2

=1 - sinB^2 - sinA^2

=cosB^2 - sinA^2

Hope this helps.

Answer 2

(cosAcosB + sinAsinB)(cosAcosB - sinAsinB) <--- difference of squares pattern

cos(A+B)cos(A-B) <-- angle addition/subtraction formulae for cosine; commutative multiplication