Page 7 - 11-Math-10 Trigonometric Identities

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= 0 . cosθ -1 . sin θ  sin 2π = 0
cos 2π = 1

= - sin θ (viii)

9) tan(a + b ) = sin(a + b=) sina cos b + cosa sin b
cos(a + b ) cosa cos b - sina sin b

sina cos b + cosa sin b  Dividing 
neumerator and
= cosa cos b cosa cos b  denuminator 
cosa cos b sina sin b
-
cosa cos b cosa cos b -cos a cos b 


∴ tan(a + b ) =tana + tan b (ix)
1- tana tan b

10) tan(a - b )= sin(a -=b ) sina cos b - cosa sin b
cos(a - b ) cosa cos b + sina sin b

sina cos b - cosa sin b  Dividing 
cosa cos b cosa cos b neumerator and
= cosa cos b + sina sin b  denuminator 

cosa cos b cosa cos b

∴ tan(a - b ) =tana - tan b (x)
1+ tana tan b

10.3 Trigonometric Ratios of Allied Angles

The angles associated with basic angles of measure θ to a right angle or its multiples
are called allied angles. So, the angles of measure 90° ± θ , 180° ± θ , 270° ± θ , 360° ± θ , are
known as allied angles.
Using fundamental law, cos(a - b ) = cos a cos b + sin a sin b and its deductions, we
derive the following identities:

version: 1.1

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