Important Trigonometric Formulas, Cheat Sheet of Trigonometry

Download Important Trigonometric Formulas and more Cheat Sheet Trigonometry in PDF only on Docsity! Important Trigonometric Formulas Textbook of Algebra and Trigonometry for Class XI ● 2 2sin cos 1θ θ+ = ● 2 21 tan secθ θ+ = ● 2 21 cot cscθ θ+ = ● sin( ) sinθ θ− = − ● cos( ) cosθ θ− = ● tan( ) tanθ θ− = − … … … … … …… … … …… … … …… … … … …… … … …… … … …… … … … … …… … … …… … … …… … … … …… … … …… ● ( )sin sin cos cos sinα β α β α β+ = + ● ( )sin sin cos cos sinα β α β α β− = − ● ( )cos cos cos sin sinα β α β α β+ = − ● ( )cos cos cos sin sinα β α β α β− = + ● ( ) tan tantan 1 tan tan α βα β α β ++ = − ● ( ) tan tantan 1 tan tan α βα β α β −− = + ……………………………………………………………………………………………………………………………………… ● sin 2 2sin cosθ θ θ= ● 2 2cos 2 cos sinθ θ θ= − ● 2 2tantan 2 1 tan θθ θ = − ……………………………………………………………………………………………………………………………………… ● 2 1 cossin 2 2 θ θ−= ● 2 1 coscos 2 2 θ θ+= ● 2 1 costan 2 1 cos θ θ θ −= + ……………………………………………………………………………………………………………………………………… ● 3sin3 3sin 4sinθ θ θ= − ● 3cos3 4cos 3cosθ θ θ= − ● 3 2 3tan tantan3 1 3tan θ θθ θ −= − ……………………………………………………………………………………………………………………………………… ● 2 2tansin 2 1 tan θθ θ = + ● 2 2 1 tancos 2 1 tan θθ θ −= + ……………………………………………………………………………………………………………………………………… ● ( ) ( )sin sin 2sin cosα β α β α β+ + − = ● ( ) ( )sin sin 2cos sinα β α β α β=+ − − ● ( ) ( )cos cos 2cos cosα β α β α β+ + − = ● ( ) ( )cos cos 2sin sinα β α β α β+ − − = − ……………………………………………………………………………………………………………………………………… ● sin sin 2sin cos 2 2 θ φ θ φθ φ + −+ = ● sin sin 2cos sin 2 2 θ φ θ φθ φ + −− = ● cos cos 2cos cos 2 2 θ φ θ φθ φ + −+ = ● cos cos 2sin sin 2 2 θ φ θ φθ φ + −− = − ……………………………………………………………………………………………………………………………………… ● ( )1 1 1 2 2sin sin sin 1 1A B A B B A− − −+ = − + − ● ( )1 1 1 2 2sin sin sin 1 1A B A B B A− − −− = − − − ● ( ) ( )1 1 1 2 2cos cos cos 1 1A B AB A B− − −      + = − − − ● ( ) ( )1 1 1 2 2cos cos cos 1 1A B AB A B− − −      − = + − − ● 1 1 1tan tan tan 1 A BA B AB − − − ++ = − ● 1 1 1tan tan tan 1 A BA B AB − − − −− = + ……………………………………………………………………………………………………………………………………… Three Steps to solve sin 2 n π θ ⋅ ±    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 2 n π θ⋅ ± is lying if it is in Ist or IInd quadrant the answer 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 667o = ( )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 quadrant therefore answer will be in negative. i.e sin 667 cos37= −o o Similar technique is used for other trigonometric ratios. i.e tan cot€ and sec csc€ . ………………………………………………………………………………………………………………………………………