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

Sir,
 
My doubt is for you, while explaining the first vedio of complementary angles in trigonometry you have solved one question that is express sin81 +cos81 in terms of trigo ratios of angles lying between 0 and 45
 
the answer is 
 
sin81 + cos81
 
sin(90-9) + cos(90-9)
 
=cos9 + sin9
 
how the solution has came i didn't understand pleae clear my doubt as soon as possible.

Asked by sana 20th October 2015, 11:57 AM
Answered by Expert
Answer:
C o n s i d e r space t h e space r i g h t space t r i a n g l e space triangle A B C space r i g h t space a n g l e d space a t space B. L e t space theta space b e space t h e space a n g l e space angle B C A comma space theta equals angle B C A T h u s comma space angle B A C equals 90 degree minus angle B C A equals 90 degree minus theta therefore sin theta equals fraction numerator o p p over denominator h y p end fraction equals fraction numerator A B over denominator A C end fraction... left parenthesis 1 right parenthesis N o w space c o n s i d e r comma space cos open parentheses 90 degree minus theta close parentheses colon space c o s open parentheses 90 degree minus theta close parentheses equals fraction numerator A B over denominator A C end fraction... left parenthesis 2 right parenthesis F r o m space e q u a t i o n s space left parenthesis 1 right parenthesis space a n d space left parenthesis 2 right parenthesis comma space w e space h a v e comma sin theta equals cos open parentheses 90 degree minus theta close parentheses equals fraction numerator A B over denominator A C end fraction.. left parenthesis 3 right parenthesis S i m i l a r l y comma space cos theta equals fraction numerator a d j over denominator h y p end fraction equals fraction numerator B C over denominator A C end fraction... left parenthesis 4 right parenthesis A n d space c o n s i d e r comma sin open parentheses 90 degree minus theta close parentheses colon sin open parentheses 90 degree minus theta close parentheses equals fraction numerator B C over denominator A C end fraction... left parenthesis 5 right parenthesis F r o m space e q u a t i o n s space left parenthesis 4 right parenthesis space a n d space left parenthesis 5 right parenthesis comma space w e space h a v e comma cos theta equals sin open parentheses 90 degree minus theta close parentheses equals fraction numerator B C over denominator A C end fraction.. left parenthesis 6 right parenthesis F r o m space e q u a t i o n s space left parenthesis 3 right parenthesis space a n d space left parenthesis 6 right parenthesis comma space w e space h a v e comma s i n theta equals c o s open parentheses 90 degree minus theta close parentheses space a n d space c o s theta equals s i n open parentheses 90 degree minus theta close parentheses
Answered by Expert 20th October 2015, 2:54 PM
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