Here, I am with another post which is very helpful to learn something not for my local country overall in the world because there is a huge scope of Mathematics that's why I thought to bring something new and helpful for my all steemians.

i. (α+в)²= α²+2αв+в²
ii. (α+в)²= (α-в)²+4αв
iii. (α-в)²= α²-2αв+в²
iv. (α-в)²= (α+в)²-4αв
v. α² + в²= (α+в)² - 2αв.
vi. α² + в²= (α-в)² + 2αв.
vii. α²-в² =(α + в)(α - в)
viii. 2(α² + в²) = (α+ в)² + (α - в)²
ix. 4αв = (α + в)² -(α-в)²
x. αв ={(α+в)/2}²-{(α-в)/2}²
xi. (α + в + ¢)² = α² + в² + ¢² + 2(αв + в¢ + ¢α)
xii. (α + в)³ = α³ + 3α²в + 3αв² + в³
xiii. (α + в)³ = α³ + в³ + 3αв(α + в)
xiv. (α-в)³=α³-3α²в+3αв²-в³
xv. α³ + в³ = (α + в) (α² -αв + в²)
xvi. α³ + в³ = (α+ в)³ -3αв(α+ в)
xvii. α³ -в³ = (α -в) (α² + αв + в²)
xviii. α³ -в³ = (α-в)³ + 3αв(α-в)
xix. ѕιη0° =0
xx. ѕιη30° = 1/2
xxi. ѕιη45° = 1/√2
xxii. ѕιη60° = √3/2
xxiii. ѕιη90° = 1
xxiv. ¢σѕ ιѕ σρρσѕιтє σƒ ѕιη
xxv. тαη0° = 0
xxvi. тαη30° = 1/√3
xxvii. тαη45° = 1
xxviii. тαη60° = √3
xxix. тαη90° = ∞
xxx. ¢σт ιѕ σρρσѕιтє σƒ тαη
xxxi. ѕє¢0° = 1
xxxii. ѕє¢30° = 2/√3
xxxiii. ѕє¢45° = √2
xxxiv. ѕє¢60° = 2
xxxv. ѕє¢90° = ∞
xxxvi. ¢σѕє¢ ιѕ σρρσѕιтє σƒ ѕє¢
xxxvii. 2ѕιηα¢σѕв=ѕιη(α+в)+ѕιη(α-в)
xxxviii. 2¢σѕαѕιηв=ѕιη(α+в)-ѕιη(α-в)
xxxix. 2¢σѕα¢σѕв=¢σѕ(α+в)+¢σѕ(α-в)
XL. 2ѕιηαѕιηв=¢σѕ(α-в)-¢σѕ(α+в)
XLi. . ѕιη(α+в)=ѕιηα ¢σѕв+ ¢σѕα ѕιηв.
XLii. » ¢σѕ(α+в)=¢σѕα ¢σѕв - ѕιηα ѕιηв.
XLiii. » ѕιη(α-в)=ѕιηα¢σѕв-¢σѕαѕιηв.
XLiv. » ¢σѕ(α-в)=¢σѕα¢σѕв+ѕιηαѕιηв.
XLv. » тαη(α+в)= (тαηα + тαηв)/ (1−тαηαтαηв)
XLvi. » тαη(α−в)= (тαηα − тαηв) / (1+ тαηαтαηв)
XLvii. » ¢σт(α+в)= (¢σтα¢σтв −1) / (¢σтα + ¢σтв)
XLviii. » ¢σт(α−в)= (¢σтα¢σтв + 1) / (¢σтв− ¢σтα)
XLix. » ѕιη(α+в)=ѕιηα ¢σѕв+ ¢σѕα ѕιηв.
L. » ¢σѕ(α+в)=¢σѕα ¢σѕв +ѕιηα ѕιηв.
Lii. » ѕιη(α-в)=ѕιηα¢σѕв-¢σѕαѕιηв.
Liii. » ¢σѕ(α-в)=¢σѕα¢σѕв+ѕιηαѕιηв.
Liv. » тαη(α+в)= (тαηα + тαηв)/ (1−тαηαтαηв)
Lv. » тαη(α−в)= (тαηα − тαηв) / (1+ тαηαтαηв)
Lvi. » ¢σт(α+в)= (¢σтα¢σтв −1) / (¢σтα + ¢σтв)
Lvii. » ¢σт(α−в)= (¢σтα¢σтв + 1) / (¢σтв− ¢σтα)
Lviii. α/ѕιηα = в/ѕιηв = ¢/ѕιη¢ = 2я
Lix. » α = в ¢σѕ¢ + ¢ ¢σѕв
Lx. » в = α ¢σѕ¢ + ¢ ¢σѕα
Lxi. » ¢ = α ¢σѕв + в ¢σѕα
Lxii » ¢σѕα = (в² + ¢²− α²) / 2в¢
Lxiii. » ¢σѕв = (¢² + α²− в²) / 2¢α
Lxiv. » ¢σѕ¢ = (α² + в²− ¢²) / 2¢α
Lxv. » Δ = αв¢/4я
Lxvi. » ѕιηΘ = 0 тнєη,Θ = ηΠ
Lxvii. » ѕιηΘ = 1 тнєη,Θ = (4η + 1)Π/2
Lxviii. » ѕιηΘ =−1 тнєη,Θ = (4η− 1)Π/2
Lxix. » ѕιηΘ = ѕιηα тнєη,Θ = ηΠ (−1)^ηα

Lxx. ѕιη2α = 2ѕιηα¢σѕα
Lxxi. ¢σѕ2α = ¢σѕ²α − ѕιη²α
Lxxii. ¢σѕ2α = 2¢σѕ²α − 1
Lxxiii. ¢σѕ2α = 1 − ѕιη²α
Lxxiv. 2ѕιη²α = 1 − ¢σѕ2α
Lxxv. 1 + ѕιη2α = (ѕιηα + ¢σѕα)²

I hope this material will be helpful for getting improvement in your subject

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