TRIGONOMETRIC FORMULA FOR CLASS 10TH

Trigonometric Formula:-

Ø  Sin A = 1/Cosec A            OR       Cosec A= 1/Sin A

Ø  Cos A = 1/Sec A               OR       Sec A = 1/ Cos A

Ø  Tan A = 1/Cot A              OR       Cot A = 1/Tan A

Ø  Tan A = Sin A/Cos A      OR       Cot A = Cos A/Sin A                                                                               

     Sin 2A = 2Sin A Cos A  = 2 Tan A /1+Tan ²A

Ø  Cos 2A = Cos ²A – Sin ²A = 1 – 2Sin ²A =  2 Cos ²A -1 =  1- Tan ²A/1+ Tan ²A

Ø  Tan 2A = 2 Tan A/1-Tan ²A

Sin 3A = 3Sin A – 4Sin³A

Cos 3A = 4 Cos ³A – 3 Cos A

Tan 3A = 3Tan A – Tan³A/1- 3Tan² A

    Sin (A+B) = Sin A. Cos B + Cos A. Sin B

Ø  Sin (A-B) = Sin A. Cos B - Cos A. Sin B

Ø  Cos (A+B) = Cos A. Cos B - Sin A. Sin B

Ø  Cos (A-B) = Cos A. Cos B + Sin A. Sin B

Ø  Tan (A+B) = Tan A + Tan B/1- Tan A Tan B

Ø  Tan (A-B) = Tan A - Tan B/1+ Tan A Tan B

Ø  Cot (A+B) =  Cot B. Cot A -1/ Cot B +Cot A

Ø  Cot (A-B) =  Cot B. Cot A +1/ Cot B -Cot A

Sin C + Sin D =  2 Sin (C+D/2) .Cos ( C-D/2)

Sin C - Sin D =  2 Cos (C+D/2) . Sin ( C-D/2)

Cos C + Cos D =  2 Cos (C+D/2) .Cos ( C-D/2)

Cos C - Cos D =  2 Sin (C+D/2) . Sin ( D-C/2)

Trigonometric Equations:-

v                 Sin ²A + Cos ²A = 1

v                 Sec ²A - Tan ²A = 1

v                Cosec² A – Cot² A = 1

  Angles:-

Sin (90-A) = Cos A

Cos (90-A) = Sin A

Tan (90-A) = Cot A

Cot (90-A) = Tan A

Sec (90-A) = Cosec A

Cosec (90-A) = Sec A