Question

If cosA+sinB=m and sinA+cosB=n, prove that 2sin(A+B)=m²+n²-2​

Answer 1

just apply some trigonometric formula.

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Answer 2

Given :

$\cos A + \sin B = m \\\\\sin A + \cos B = n$

To prove : $2 sin (A+B) = m^2+n^2-2$

Solution:

$\cos A + \sin B = m..(1) \\\\\sin A + \cos B = n..(2)$

solving RHS :

using 1 and 2

$m^2 +n^2 -2\\\\(\cos A +\sin B )^2+(\sin A +\cos B )^2-2\\\\\cos ^2A+\sin ^2B +2\cos A \sin B +\sin ^2A+\cos^2B+2\sin A +\cos B -2 \\\\(\sin ^2A+\cos^2A)+(\sin ^2B+\cos^2B)+2 (\sin A \cos B+\cos A +\sin B)-2\\\\1+1+2\sin (A+B)-2\\\\2\sin(A+B)\\\\2\sin(A+B)=LHS$

LHS= RHS

hence proved

#Learn more :

https://brainly.in/question/2182588