Question

It's a question of trigonometry. Evaluate: sin(50°+θ) – cos (40° – θ) + tan 10°tan 20°tan70°tan80°. Please give the correct answer ^_^

Answer 1

Answer:

The value of the expression is 1.

Step-by-step explanation:

Formula

1. sinθ = cos(90-θ)

2. tanθ = cot(90-θ)

3. cotθ = 1/tanθ

Calculation

The given expression is

sin(50º+θ)-cos(40º-θ)+ tan10ºtan20ºtan70ºtan80º

or cos(90º-(50º+θ)) - cos(40º-θ)+ tan10ºtan20ºcot(90º-70º)cot(90º-80º)

or cos(40º-θ) - cos(40º-θ)

+ tan10ºtan20ºcot20ºcot10º

or 0 + tan10ºtan20º*(1/tan20º)*(1/tan10º)

or (tan10º/tan10º)*(tan20º/tan20º)

= 1*1 = 1