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If cos A+sin B=m and sin A+cos B=n , pr...

If `cos A+sin B=m` and `sin A+cos B=n ,` prove that `2sin(A+B)=m^2+n^2-2.`

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Given `cosA + sinB = m and sinA + cosB = n `
RHS `= m^2 + n^2 – 2` ` =(cosA + sinB)^2 +(sinA + cosB)^2 – 2 `
`= cos^2A + sin^2B + 2 cosA sinB + sin^2A + cos^2B + 2 sinA cosB – 2 `
`= 1 + 1 + 2(cosA sinB + sinA cosB) - 2 ` ...
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RD SHARMA-TRIGONOMETRIC RATIOS OF COMPOUND ANGLES-Solved Examples And Exercises
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