Question

SinA + cosA=mand sin^3A+cos^3A=n prove that m^3-3m+2n=0

Answer 1

Given: sinA + cosA=m and sin^3A+cos^3A=n

To find: Prove that m^3-3m+2n=0

Solution:

• Now we have given

                sinA + cosA = m

                sin^3A + cos^3A = n

• expanding the term, we get:

                (sin A + cos A)(sin²A + cos²A - sinAcosA) = n

                (sin A + cos A)(sin²A + cos²A - sinAcosA ) = n...................(i)

• Now we have sinA + cosA = m

• Squaring on both sides, we get:

                sin²A + cos²A + 2 sinAcosA = m²

                sinAcosA = m²-1/2             ..................(ii)

• Putting ii in i, we get:

                m x (1 - (m²-1)/2 )  = n

                m x (2-m^2+1 / 2) = n

                m x (3-m^2 / 2) = n

                3m - m^3 = 2n

• Taking all the terms on one side, we get:

                m^3 - 3m + 2n = 0

Answer:

               So we have proved that m^3 - 3m + 2n = 0.

Answer 2

Refer to the above attachment for your ans.....

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