Question
what is another form of: sin (A+B) sin (A-B)/ cos^2 A cos^2 B
a) cos^2 A - cos^2 B
b) tan^2 A - tan^2 B
c) tan^2 A - tan^2 B
d) sin^2 A - sin^2 B
please show the steps you take to get to the answer! thank you
a) cos^2 A - cos^2 B
b) tan^2 A - tan^2 B
c) tan^2 A - tan^2 B
d) sin^2 A - sin^2 B
please show the steps you take to get to the answer! thank you
Answers
Damon
sin (a+b) = sin a cos b + cos a sin b
sin (a-b) = sin a cos b - cos a sin b
product
sin^2 a cos^2 b - cos^2 a sin^2 b
now divide by cos^2 a cos^2 b
sin^2 a/cos^2a - sin^2 b/ cos^2 b
= tan^2 a - tan^2 b
sin (a-b) = sin a cos b - cos a sin b
product
sin^2 a cos^2 b - cos^2 a sin^2 b
now divide by cos^2 a cos^2 b
sin^2 a/cos^2a - sin^2 b/ cos^2 b
= tan^2 a - tan^2 b