Let's simplify the expression step by step:
tg 7α - tg 2α ÷ 1 + tg 7α · tg 2= (tg 7α - tg 2α) / (1 + tg 7α · tg 2α)
We know that tg(a) - tg(b) = sin(a)cos(b) - cos(a)sin(b) = sin(a-bTherefore, tg 7α - tg 2α = sin(7α - 2α) = sin(5α)
Similarly, we know that tg(a) · tg(b) = sin(a)cos(a) / cos(b)sin(b) = sin(2a)cos(2bTherefore, tg 7α · tg 2α = sin(14α)cos(4α)
Now, let's simplify the expression further:
= (sin(5α)) / (1 + sin(14α)cos(4α))
This is the simplified form of the given expression: (sin(5α)) / (1 + sin(14α)cos(4α))
Let's simplify the expression step by step:
tg 7α - tg 2α ÷ 1 + tg 7α · tg 2
= (tg 7α - tg 2α) / (1 + tg 7α · tg 2α)
We know that tg(a) - tg(b) = sin(a)cos(b) - cos(a)sin(b) = sin(a-b
Therefore, tg 7α - tg 2α = sin(7α - 2α) = sin(5α)
Similarly, we know that tg(a) · tg(b) = sin(a)cos(a) / cos(b)sin(b) = sin(2a)cos(2b
Therefore, tg 7α · tg 2α = sin(14α)cos(4α)
Now, let's simplify the expression further:
= (sin(5α)) / (1 + sin(14α)cos(4α))
This is the simplified form of the given expression: (sin(5α)) / (1 + sin(14α)cos(4α))