Question

What is the value of [(sin 7x – sin 5x)÷(cos 7x + cos 5x)] – [(cos 6x – cos 4x)÷(sin 6x + sin 4x)]?

Answer 1

Answer:

2tanx

Step-by-step explanation:

[(sin 7x – sin 5x)÷(cos 7x + cos 5x)] – [(cos 6x – cos 4x)÷(sin 6x + sin 4x)]

sinA+sinB=2sin(A+B/2).cos(A+B/2)

sinA-sinB=2cos(A+B/2).sin(A+B/2)

cosA+cosB=2cos(A+B/2).cos(A-B/2)

cosA-cosB= -2sin(A+B/2).sin(A-B/2)

now,

sin7x-sin5x = 2cos6x.sinx

cos7x+cos5x = 2cos6x.cosx

cos6x-cos4x = -2sin5x.sinx

sin6x+sin4x = 2sin5x.cosx

putting these values in the given problem, we get,

((2cos6x.sinx)÷(2cos6x.cosx))-((-2sin5x.sinx)÷(2sin5x.cosx))

sinx/cosx + sinx/cosx

tanx + tanx

2tanx