Question:
could u please prove all the trigonometric formulaes
Answer:
In trigonometry, there are a lot of formulas. We can not write all formulas but we are
listing some important formulas.
1. Trigonometric functions
sin α, cos α
tan α = sin α/cos α, α ≠ π/2 + nπ, n ∈ Z
cot α = cos α/sin α, α ≠ π + nπ, n ∈ Z
tan α * cot α = 1
sec α = 1/cos α, α ≠ π/2 + nπ, n ∈ Z
cosec α = 1/sin α, α ≠ π + nπ, n ∈ Z
2. Pythagorus Identiy:
sin2 α + cos2 α = 1
1 + tan2 α = sec2 α
1 + cot2 α = cosec2 α
3. Sum-Difference Formula:
sin (α + β) = sin α * cos β + cos α * sin β
sin (α - β) = sin α * cos β - cos α * sin β
cos (α + β) = cos α * cos β - sin α * sin β
cos (α - β) = cos α * cos β + sin α * sin β
tan (α + β) = (tan α + tan β)/(1 - tan α * tan β)
tan (α - β) = (tan α - tan β)/(1 + tan α * tan β)
Rest of formulas, you can see from the book or on our website.
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