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Complementary Angles
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COMPLEMENTARY ANGLE: Two angles are said to be complementary, if their sum is 90.
It follows from the above definition that the and (90 - ) are complementary angles.

TRIGONOMETRIC RATIOS OF COMPLEMENTARY ANGLES
THEOREM
If  is an acute angle, then prove that
sin (90 - ) = cos , cos (90 - ) = sin ,
tan (90 - ) = cot , cot (90 - 9) = tan ,
sec (90 - ) = cosec and, cosec (90 - ) = sec
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Example: Prove that
cosec2 (90 - ) - tan2 = cos2 (90 - ) + cos2
Solution: you have,
LHS = cosec2(90 - ) - tan2                 [cosec (90 - ) = sec]
        = sec2 - tan2
        = 1                                             [sec2 - tan2 = 1]
and,
RHS = cos2 (90- ) + cos2
        = sin2 +cos2                             [cos (90 - ) = sin]
        = 1
Hence, LHS = RHS
 
   
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