Question

यदि A, B और C धनात्मक न्यूनकोण इस प्रकार हैं कि
sin (A+ B- C)=1/2
cos (B+C - A)=1/2
tan (A+ C - B) = 1, तो A B तथा C के मान ज्ञात कीजिए।
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Answer 1

Answer:

A= 37.5 ;. B=45;;. C=52.5

Step-by-step explanation:

as we know

sin(a+b-c)=1/2

and it is known that sin30°=1/2

so, sin(a+b-c)=sin30°

hence

a+b-c =30° ------------------(1)

secondly we are given that cos(b+c-a)=1/2

we know cos 60° is also 1/2

hence

cos60°=cos(b+c-a)

60=b+c-a-----------(2)

thirdly we are given with tan (a+c-b)=1

tan 45°is also 1

hence 45=a+c-b-----------(3)

now let the value of a=30+c-b "from equation (1)

put this value of a in equation (2)

it would come b=45

now put the value of a in equation (3)

it would result in value of c

i.e. 52.5

and at last put value of b and c value of a will come i.e. 37.5