How do you find the exact value of cos40sin55cos55sin40 using the sum and difference, double angle or half angle formulas?

1 Answer

3122

Explanation:

Use trigonometric identity:
cos(a+b)=cosacosbsinasinb, we have
sin(5540)=sin55cos40sin40cos55=sin15

Find sin15, by using trigonometric identity:

2sin2(15)=1cos30=132=232
sin2(15)=234
sin(15)=±232

Only the positive value is accepted because sin15 is positive.

Finally,
cos40.sin55cos55.sin40=sin15=232

= 42322

= (3)2+122322

= 3122