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Home / Doubts and Solutions/ANDHRA PRADESH/Class 10/Mathematics

I want the step by step proof for why sin90+x=cosx? with appropriate digrams in each step.
CLUE: we have a good and reasonal proof for sin90_x=cosx. i want it in a similar way.
thank u.
 
 

Asked by eswarpremsai9i 5th July 2015, 10:25 PM
Answered by Expert
Answer:
C o n s i d e r space t h e space f o l l o w i n g space g r a p h.
L e t space O A space b e space a space r a y space m a k i n g space a n space a n g l e space theta space w i t h space t h e space X minus a x i s. L e t space P open parentheses x comma y close parentheses space b e space a n y space p o i n t space o n space t h e space r a y space O A. rightwards double arrow angle A O Q equals angle P O Q equals theta A n d space O Q equals x space a n d space P Q equals y L e t space Q space b e space t h e space f o o t space o f space p e r p e n d i c u l a r space o f space P space o n space t h e space X minus a x i s. N o w space l e t space u s space d r a w space a space r a y space O B space s u c h space t h a t space angle A O B equals 90 degree rightwards double arrow angle P O R equals 90 degree M a r k space a space p o i n t space R space o n space O B space s u c h space t h a t space O R equals O P equals r D r o p space a space p e r p e n d i c u l a r space f r o m space R space o n space t h e space X minus a x i s space a n d space l e t space S space b e space t h e space f o o t space o f space t h e space p e r p e n d i c u l a r. I t space i s space c l e a r space f r o m space t h e space d i a g r a m space t h a t space O Q P space i s space c o n g r u e n t space t o space R S O space T h e r e f o r e comma space S O equals P Q equals y space a n d space R S equals O Q equals x S o space t h e space c o o r d i n a t e s space o f space R space a r e space open parentheses negative y comma x close parentheses H e n c e comma space sin open parentheses 90 degree plus theta close parentheses equals fraction numerator R S over denominator O R end fraction equals x over r equals cos theta T h u s comma space space s i n open parentheses 90 degree plus theta close parentheses equals cos theta
Answered by Expert 6th July 2015, 11:47 AM
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