Prove the identity tan5x Use the SumtoProduct Formulas and

Prove the identity.

= tan(5x)

Use the Sum-to-Product Formulas and then simplify.

sin(x) + sin(9x)

cos(x) + cos(9x)

19. -3 points SPreCalc 7.3.089 My No Prove the identity. sin(x) +sin(9x) 5x) = tan(5x) cos(x) + cos(3x) Use the Sum-to-Product Formulas and then simplify sin(x) sin(9x 2 cos(x) cos(x) 2 cos(5x) cos(4x) cosx) 5 Need Help?Read tWatch It

Solution

( sin x + sin 9x ) / ( cos x + cos 9x ) = 2 sin ( 9x + x) /2 cos ( 9x - x ) /2

= 2 sin ( 5x ) cos (4x )

= 2 ( sin (5x ) cos (4x ) ) / 2 cos (5x ) cos (4x)

= sin (5x ) / cos (5x )

= tan (5x )

proved !