Fsc Trigonometric Formulas

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Important Trigonometric Formulas Textbook of Algebra and Trigonometry for Class XI Available online @ http://www.mathcity.org, Version: 1.0.2

● sin 2 θ + cos2 θ = 1 ● sin(−θ ) = − sin θ

● 1 + tan 2 θ = sec2 θ ● cos(−θ ) = cosθ

● 1 + cot 2 θ = csc2 θ ● tan( −θ ) = − tan θ

………………………………………………………………………………………………………………………………………

● sin (α + β ) = sin α cos β + cosα sin β

● sin (α − β ) = sin α cos β − cosα sin β

● cos (α + β ) = cosα cos β − sin α sin β ● tan (α + β ) =

● cos (α − β ) = cosα cos β + sin α sin β

tan α + tan β 1 − tan α tan β

● tan (α − β ) =

tan α − tan β 1 + tan α tan β

………………………………………………………………………………………………………………………………………

● sin 2θ = 2sinθ cosθ

● cos 2θ = cos2 θ − sin 2 θ

● tan 2θ =

2 tanθ 1 − tan 2 θ

………………………………………………………………………………………………………………………………………

● sin 2 ●

θ 1 − cosθ = 2 2

● cos 2

θ 1 + cosθ = 2 2

● tan 2

θ 1 − cosθ = 2 1 + cosθ

……………………………………………………………………………………………………………………………………… 3tan θ − tan 3 θ 3 3 ● cos3θ = 4cos θ − 3cosθ ● tan 3θ = sin 3θ = 3sin θ − 4sin θ 2

1 − 3tan θ

……………………………………………………………………………………………………………………………………… 2

● sin 2θ =

2tan θ 1 + tan 2 θ

● cos 2θ =

1 − tan θ 1 + tan 2 θ

………………………………………………………………………………………………………………………………………

● sin (α + β ) + sin (α − β ) = 2sin α cos β

● cos (α + β ) + cos (α − β ) = 2cosα cos β

● sin (α + β ) − sin (α − β ) = 2cosα sin β

● cos (α + β ) − cos (α − β ) = −2sin α sin β

………………………………………………………………………………………………………………………………………

θ +φ θ −φ cos 2 2 θ +φ θ −φ cos ● cosθ + cosφ = 2cos 2 2

θ +φ θ −φ sin 2 2 θ +φ θ −φ ● cosθ − cos φ = −2sin sin 2 2

● sin θ + sin φ = 2sin

● sin θ − sin φ = 2cos

………………………………………………………………………………………………………………………………………

( ( A 1− B

) − B 1− A )

● sin −1 A + sin −1 B = sin −1 A 1 − B 2 + B 1 − A2 ● sin −1 A − sin −1 B = sin −1

 ● cos −1 A + cos −1 B = cos−1  AB −   ● cos −1 A − cos −1 B = cos−1  AB +  ● tan −1 A + tan −1 B = tan −1

A+ B 1 − AB

2

2

(1 − A )(1 − B )  2

2

(1 − A )(1 − B )  2

2

● tan −1 A − tan −1 B = tan −1

A− B 1 + AB

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 

Three Steps to solve sin  n ⋅

π  ±θ  2 

Step I: First check that n is even or odd Step II: If n is even then the answer will be in sin and if the n is odd then sin will be converted to cos and vice virsa (i.e. cos will be converted to sin). Step III: Now check in which quadrant n ⋅

π ± θ is lying if it is in Ist or IInd quadrant the answer 2

will be positive as sin is positive in these quadrants and if it is in the IIIrd or IVth quadrant the answer will be negative. e.g. sin 667 o = sin ( 7(90) + 37 ) Since n = 7 is odd so answer will be in cos and 667 is in IVth quadrant and sin is –ive in IVth o o quadrant therefore answer will be in negative. i.e sin 667 = − cos37 Similar technique is used for other trigonometric ratios. i.e tan € cot and sec € csc . ……………………………………………………………………………………………………………………………………… Made By: Atiq ur Rehman Email: [email protected] Corrected by: Salman Zaidi

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