Assertion (A):If A =10^ , B =16^ , C =19^ , then 2 ~A 2 ~B + 2 ~B 2 C + 2 C 2 ~A =1 . Reason (R): If A+B+C=180^ ,= A 2 B 2 C 2 = A 2 ~B 2 C 2 Which of the following is correct?

Question

Quantrex Academy · Accepted Answer

Correct answer: A. Both (A) and (R) are true and (R) is the correct explanation of (A)

Given that A=10^ , B=16^ and C=19^ A+B+C=45^ 2 A+2 B+2 C=90^ ...(i) We know that, (2 A+2 B+2 C) aligned & = 2 A+ 2 B+ 2 C- 2 A 2 B 2 C 1- 2 A 2 B- 2 B 2 C- 2 C 2 A & = 2 A+ 2 B+ 2 C- 2 A 2 B 2 C 1- 2 A 2 B- 2 B 2 C- 2 C 2 A & 2 A 2 B+ 2 B 2 C+ 2 C 2 A=1 aligned So, Assertion is correct. Now divide by 2 A 2 B 2 C both side aligned & 1 2 A + 1 2 B + 1 2 C = 1 2 A 2 B 2 C & 2 A+ 2 B+ 2 C= 2 A 2 B 2 C & A 2 + B 2 + C 2 = A 2 B 2 C 2 aligned Also A+B+C=180^ [from (i)] So, Reason is correct.

Assertion (A):If A =10^ , B =16^ , C =19^ , then 2 ~A 2 ~B + 2 ~B 2 C + 2 C 2 ~A =1 . Reason (R): If A+B+C=180^ ,= A 2 B 2 C 2 = A 2 ~B 2 C 2 Which of the following is correct?

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Correct answer

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