Question

सिद्ध कीजिए कि- sin{(n+1)A}.sin{(n+2)A}+cos{(n+1)A}.cos{(n+2)A}=cosA.

Answer 1

Answer:

CosA

Step-by-step explanation:

Prove that -

Sin{(n+1)A}.Sin{(n+2)A} + Cos{(n+1)A}.Cos{(n+2)A} = CosA

L.H.S.    

= Sin{(n+1)A}.Sin{(n+2)A} + Cos{(n+1)A}.Cos{(n+2)A}

= Sin(nA+A).Sin(nA+2A) + Cos(nA+A).Cos(nA+2A)

= Cos(nA+2A).Cos(nA+A) + Sin(nA+2A).Sin(nA+A)

Using Formula-

Cos(A+B) = CosA.CosB - SinA.SinB

So, Cos(nA+2A).Cos(nA+A) + Sin(nA+2A).Sin(nA+A)

= Cos{(nA+2A) - (nA+A)}

= Cos(nA + 2A - nA - A)

= CosA

= R.H.S.

Hence Proved

Answer 2

Answer:

please mark as a brainliest answer

Step-by-step explanation:

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