Question

If sin(A+B)=1 cos(A-B)=root 3/2 then find A&B
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Answer 1

Question:

If sin(A+B)=1 cos(A-B)=root 3/2 then find the value A and B.

Answer:

Given,

$sin(a + b) = 1 \\ \\ cos(a - b) = \frac{ \sqrt{3} }{2}$

Find,

$sin(a + b) = 1 \\ \\ sin(a + b) = sin90 \degree \\ \\ a + b = 90 \degree............(1) \\ \\ cos(a - b) = \frac{ \sqrt{3} }{2} \\ \\ cos(a - b) = cos30 \degree \\ \\ a - b = 30 \degree............(2)$

from 1 and 2,

$a + b = 90 \degree \\ a - b = 30 \degree \\ ................... \\ 2a \: \: \: \: \: = 120 \degree$

$a = 60 \degree$

put value of a =60 in 1

$a + b = 90 \degree \\ \\ 60 + b = 90 \degree \\ \\ b = 90 - 60 \\ \\ b = 30$

Hence the value of a =60 and b=30