Question

How to simplify?
5 sin alpha tan alpha cos alpha

Answer 1

What is trigonometry ?

  Trigonometry is the study of angles and the ratios of sine, cosine, tangent, cosec, sectant and cot. It includes a number of trigonometric identity laws and some relation between ratios.

Some of the laws are :

    • sinθ * cosecθ = 1

    • cosθ * secθ = 1

    • tanθ * cotθ = 1

    • sin(90° - θ) = cosθ and vice versa

    • tan(90° - θ) = secθ and vice versa

    • cot(90° - θ) = cosecθ and vice versa

    • sin²θ + cos²θ = 1

    • sec²θ - tan²θ = 1

    • cosec²θ - cot²θ = 1

Now, we come to solve the problem.

∴ 5 sinα tanα cosα

= 5 sinα ( sinα / cosα ) cosα

= 5 sin²α ,

which is the required simplified form.