Trigonometry Formulae & Identities for Exams Part 3rd

Following the sequence of last post on basics of Trigonometry I am continuing the basics of Trigonometry in this post too. Let’s prepare these trigonometric formulae and identities to get full hold on the questions of trigonometry which will help in Competitive Exams.

Trigonometric Functions of Acute Angles

Sinθ = P/H

Cosθ = B/H

Tanθ = P/B

Cosecθ = H/P

Secθ = H/B

Cotθ = B/P.

Relations between Trigonometric Functions

Sinθ = 1/Cosecθ

Cosθ = 1/Secθ

Tanθ = 1/Cotθ

Cosecθ = 1/Sinθ

Secθ = 1/Cosθ

Cotθ = 1/Tanθ

Tanθ = Sinθ/Cosθ

Cotθ = Cosθ/ Sinθ

Pythagorean Identities

Sin²θ + Cos²θ = 1    →  Sin²θ = 1 - Cos²θ     →  Cos²θ = 1 -  Sin²θ    

Sec²θ - Tan²θ = 1    →  Sec²θ = 1 + Tan²θ    →  Sec²θ -  1 = Tan²θ  

  Cosec²θ - Cot²θ = 1 →  Cosec²θ = 1 + Cot²θ  →  Cosec²θ -  1 = Cot²θ  

Addition Formulas

Sin(A + B) = SinA CosB + CosA sinB 

Sin(A - B) = SinA CosB  - CosA SinB

Cos(A + B) = CosA CosB - SinA SinB

Cos(A - B) = CosA CosB + SinA SinB

Tan(A + B) = [ TanA + TanB ] / [ 1 - TanA TanB]

Tan(A + B) = [ TanA - TanB ] / [ 1 + TanA TanB]

Cot(A + B) = [ CotA CotB - 1 ] / [ CotA + CotB]

Cot(A + B) = [ CotA CotB - 1 ] / [ CotA + CotB] 

Product to Sum/Difference Formulas

SinA CosB = (1/2) [ Sin (A + B) + Sin (A - B)] 

CosA SinB = (1/2) [ Sin (A + B) - Sin (A - B)] 

CosA CosB = (1/2) [ Cos (A + B) + Cos (A - B)] 

SinA SinB = (1/2) [ Cos (A - B) - Cos (A + B)] 

Consider A+B = C and A – B = D in above Formulae

Sum to Product Formulas

SinC + SinD = 2 Sin[ (C + D) / 2 ] Cos[ (C - D) / 2 ]

CosC + CosD = 2 Cos[ (C + D) / 2 ] Cos[ (C - D) / 2 ] 

Difference to Product Formulas

SinC - SinD = 2 Cos[ (C + D) / 2 ] Sin[ (C - D) / 2 ]

CosC - CosD = 2 Sin[ (C + D) / 2 ] Sin[ (D - C) / 2 ] 

Difference of Squares Formulas

Sin ²A - Sin ²B = Sin(A + B) Sin(A - B)

Cos ²B - Cos ²A = Sin(A + B) Sin(A - B) 

Cos ²A - Sin ²B = Cos(A + B) Cos(A - B)

Cos ²B - Sin ²A = Cos(A + B) Cos(A - B)

 Hope you have enjoyed the base concept of this chapter till now. More Conceptual enjoyment will be continued for you soon, just keep visiting this blog regularly and writing me your related queries through comment or forum.

Best of Luck for Exams. To be continued soon........................