Mathematics: Class XIII

Faculty: Shukla Sir

“25 Years of Transforming Minds, Shaping Futures."

IMPORTANTFORMULA’S
00 -1800 300-1500 S A
450-1350 600-1200
900-2700 00-3600 T C

−𝛉 𝜋/2 − 𝜃 𝜋/2 + 𝜃 π−θ π+θ 2π − θ 2π + θ

𝟗𝟎𝟎 − 𝛉 𝟗𝟎𝟎 + 𝛉 𝟏𝟖𝟎𝟎 − 𝛉 𝟏𝟖𝟎𝟎 + 𝛉 𝟑𝟔𝟎𝟎 − 𝛉 𝟑𝟔𝟎𝟎 + 𝛉

Sin −Sin +Cos +Cos +Sin −Sin −Sin +Sin

Cos +Cos +Sin −Sin −Cos −Cos +Cos +Cos

Tan −Tan +Cot −Cot −Tan +Tan −Tan +Tan

Cot −Cot +Tan −Tan −Cot +Cot −Cot +Cot

Sec +Sec +Cosec −Cosec −Sec −Sec +Sec +Sec

Cosec −Cosec +Sec +Sec +Cosec −Cosec −Cosec +Cosec

𝟎𝟎 𝟑𝟎𝟎 𝟒𝟓𝟎 𝟔𝟎𝟎 𝟗𝟎𝟎 𝟏𝟐𝟎𝟎 𝟏𝟑𝟓𝟎 𝟏𝟓𝟎𝟎 𝟏𝟖𝟎𝟎 𝟐𝟕𝟎𝟎

𝑺𝒊𝒏 0 1 1 √3 1 √3 1 1 0 −1
2 √2 2 2 √2 2

𝑪𝒐𝒔 1 √3 1 1 0 −1 −1 −√3 −1 0
2 √2 2 2 √2 2

𝑻𝒂𝒏 0 1 1 √3 ∞ −√3 −1 −1 0 ∞
√3 √3

𝑪𝒐𝒕 ∞ √3 1 1 0 −1 −1 −√3 ∞ 0
√3 √3

𝑺𝒆𝒄 1 2 √2 2 ∞ −2 −√2 −2 −1 ∞
√3 √3
1

𝑪𝒐𝒔𝒆𝒄 ∞ 2 √2 2 1 2 √2 2 ∞ −1
Page

√3 √3

========================================================================================
prepared by :- Shukla Sir (Having an experience of 20+ Years in CBSE Exams Teaching)
UTTAM NAGAR: G-1/148 Opp.Metro Pillar No. 675, Uttam Nagar, N.D.-59. Call @ 706-572-1717
VIKAS PURI: A-39, First Floor, Guru Virjanand Marg, Vikas Puri, N.D.-18. Call @ 920-551-6639
 Mathematics: Class XIII
Faculty: Shukla Sir
“25 Years of Transforming Minds, Shaping Futures."

𝑆𝑖𝑛(𝐴 + 𝐵) = 𝑆𝑖𝑛𝐴 𝐶𝑜𝑠𝐵 + 𝐶𝑜𝑠𝐴𝑆𝑖𝑛𝐵 𝐶𝑜𝑠(𝐴 + 𝐵) = 𝐶𝑜𝑠𝐴 𝐶𝑜𝑠𝐵 − 𝑆𝑖𝑛𝐴 𝑆𝑖𝑛𝐵

𝑆𝑖𝑛(𝐴 − 𝐵) = 𝑆𝑖𝑛𝐴 𝐶𝑜𝑠𝐵 − 𝐶𝑜𝑠𝐴 𝑆𝑖𝑛𝐵 𝐶𝑜𝑠(𝐴 − 𝐵) = 𝐶𝑜𝑠𝐴 𝐶𝑜𝑠𝐵 + 𝑆𝑖𝑛𝐴 𝑆𝑖𝑛𝐵

𝑆𝑖𝑛(𝐴 + 𝐵) + 𝑆𝑖𝑛(𝐴 − 𝐵) = 2 𝑆𝑖𝑛𝐴 𝐶𝑜𝑠𝐵 𝐶𝑜𝑠(𝐴 + 𝐵) + 𝐶𝑜𝑠(𝐴 − 𝐵) = 2 𝐶𝑜𝑠𝐴 𝐶𝑜𝑠𝐵

𝑆𝑖𝑛(𝐴 + 𝐵) − 𝑆𝑖𝑛(𝐴 − 𝐵) = 2 𝐶𝑜𝑠𝐴 𝑆𝑖𝑛𝐵 𝐶𝑜𝑠(𝐴 + 𝐵) − 𝐶𝑜𝑠(𝐴 − 𝐵) = −2 𝑆𝑖𝑛𝐴 𝑆𝑖𝑛𝐵

𝑪+𝑫 𝑪−𝑫
Let 𝑨 + 𝑩 = 𝑪, 𝑨−𝑩=𝑫 Now 𝑨= , 𝑩=
𝟐 𝟐

𝐶+𝐷 𝐶−𝐷 𝐶+𝐷 𝐶−𝐷

𝑆𝑖𝑛𝐶 + 𝑆𝑖𝑛𝐷 = 2 𝑆𝑖𝑛 𝐶𝑜𝑠 𝐶𝑜𝑠𝐶 + 𝐶𝑜𝑠𝐷 = 2 𝐶𝑜𝑠 𝐶𝑜𝑠
2 2 2 2

𝐶+𝐷 𝐶−𝐷 𝐶+𝐷 𝐶−𝐷

𝑆𝑖𝑛𝐶 − 𝑆𝑖𝑛𝐷 = 2 𝐶𝑜𝑠 𝑆𝑖𝑛 𝐶𝑜𝑠𝐶 − 𝐶𝑜𝑠𝐷 = −2 𝑆𝑖𝑛 𝑆𝑖𝑛
2 2 2 2

𝐶+𝐷 𝐷−𝐶
𝐒 + 𝐒 = 𝟐𝐒𝐂 𝐂 + 𝐂 = 𝟐𝐂𝐂 = 2𝑆𝑖𝑛 𝑆𝑖𝑛
2 2
𝐒 − 𝐒 = 𝟐𝐂𝐒 𝐂 − 𝐂 = −𝟐𝐒𝐒

2 𝑡𝑎𝑛𝐴 2 𝑡𝑎𝑛𝐴
𝑆𝑖𝑛 2𝐴 = 2 𝑆𝑖𝑛𝐴 𝐶𝑜𝑠𝐴 = 𝑇𝑎𝑛 2𝐴 = √1 ± 𝑆𝑖𝑛2𝑥 = 𝐶𝑜𝑠𝑥 ± 𝑆𝑖𝑛𝑥
1+𝑡𝑎𝑛2 𝐴 1−𝑡𝑎𝑛2 𝐴

1−𝑡𝑎𝑛2 𝐴
𝐶𝑜𝑠 2𝐴 = 𝐶𝑜𝑠 2 𝐴 − 𝑆𝑖𝑛2 𝐴 = 2𝐶𝑜𝑠 2 𝐴 − 1 = 1 − 2𝑆𝑖𝑛2 𝐴 =
1+𝑡𝑎𝑛2 𝐴

𝑡𝑎𝑛𝐴+𝑡𝑎𝑛𝐵 𝑡𝑎𝑛𝐴−𝑡𝑎𝑛𝐵
𝑇𝑎𝑛(𝐴 + 𝐵) = 𝑇𝑎𝑛(𝐴 − 𝐵) =
1−𝑡𝑎𝑛𝐴.𝑡𝑎𝑛𝐵 1+𝑡𝑎𝑛𝐴.𝑡𝑎𝑛𝐵

3 𝑇𝑎𝑛𝑥−𝑇𝑎𝑛3 𝑥 𝜋 1 ± 𝑡𝑎𝑛𝐴
𝑇𝑎𝑛3𝑥 = 𝑇𝑎𝑛 ( ± 𝐴) =
1−3 𝑇𝑎𝑛2 𝑥 4 1 ∓ 𝑡𝑎𝑛𝐴

𝑆𝑖𝑛3𝑥 = 3 𝑆𝑖𝑛𝑥 − 4 𝑠𝑖𝑛3 𝑥 𝑐𝑜𝑠3𝑥 = 4 𝐶𝑜𝑠 3 𝑥 − 3𝐶𝑜𝑠𝑥

𝐒𝐎𝐌𝐄 𝐈𝐌𝐏𝐎𝐑𝐓𝐀𝐍𝐓 𝐏𝐑𝐎𝐏𝐄𝐑𝐓𝐘

m
𝑙𝑜𝑔 𝑚𝑛 = 𝑙𝑜𝑔 𝑚 + 𝑙𝑜𝑔 𝑛 𝑙𝑜𝑔 = log 𝑚 − 𝑙𝑜𝑔 𝑛
n

𝑙𝑜𝑔 𝑚𝑛 = 𝑛 𝑙𝑜𝑔 𝑚 𝑒 𝑙𝑜𝑔𝑥 = 𝑥

𝑙𝑜𝑔𝑎
log 𝑒 𝑒 = 1 log 𝑏 𝑎 =
𝑙𝑜𝑔𝑏

(𝑥 + 𝑦)2 = 𝑥 2 + 𝑦 2 + 2𝑥𝑦 (𝑥 + 𝑦)3 = 𝑥 3 + 𝑦 3 + 3𝑥𝑦(𝑥 + 𝑦)

(𝑥 − 𝑦)2 = 𝑥 2 + 𝑦 2 − 2𝑥𝑦 (𝑥 − 𝑦)3 = 𝑥 3 − 𝑦 3 − 3𝑥𝑦(𝑥 − 𝑦)
𝑥 2 −𝑦 2 = (𝑥 + 𝑦)(𝑥 − 𝑦) 𝑥 3 + 𝑦 3 = (𝑥 + 𝑦)(𝑥 2 + 𝑦 2 − 𝑥𝑦)
2
Page

========================================================================================
prepared by :- Shukla Sir (Having an experience of 20+ Years in CBSE Exams Teaching)
UTTAM NAGAR: G-1/148 Opp.Metro Pillar No. 675, Uttam Nagar, N.D.-59. Call @ 706-572-1717
VIKAS PURI: A-39, First Floor, Guru Virjanand Marg, Vikas Puri, N.D.-18. Call @ 920-551-6639