Which of the following is true in a triangle ABC?
Which of the following is true in a triangle ABC?
(a) (b+c) cos〖A/2=2a sin((B-C)/2) 〗
(b) (b-c) sin〖((B-C)/2)=2a cos〖A/2〗 〗
(c) (b+c) sin〖((B-C)/2)=2a cos〖A/2〗 〗
(d) (b-c) cos〖A/2=a sin((B-C)/2) 〗
Ans: d
Sol.
(b-c)/a=sin〖B-sinC 〗/sinA
=(2 sin〖((B-C)/2) cos((B+C)/2) 〗)/(2 sin〖A/2 cos〖A/2〗 〗 )=sin((B-C)/2)/cos〖A/2〗
⇒(b-c) cos〖A/2=a sin((B-C)/2) 〗
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If (27)^999 is divided by 7, then the remainder is
(a) 6 (b) 1 (c) 2 (d) 3
Ans: a
Sol.
=(28-1)^999
=⏟((_ ^999)C_0^ 28^999+⋯+(_ ^999)C_998^ 28^1 1^998 )┬(28x→is divided by 7)-(_ ^999)C_999^ 28^0 1^999
=7×N-1
=7N-1+7-7
=7N-7+7-1
=7(N-1)+6
So when (27)^999 is divided by 7 the remainder is 6
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