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Prove that sin(n+1)xsin(n+2)x+cos(n+1)xc...

Prove that `sin(n+1)xsin(n+2)x+cos(n+1)xcos(n+2)x=cosx`

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Put .(n+1) x=A. and .(n+2) x=B.
.sin (n+1) x sin (n+2) x+cos (n+1) x cos (n+2) x.
.=sin ^(prime) A sin B+cos A cos B=cos (A-B)=cos [(n+1) x-(n+2) x].
.=cos [n x+x-n x-2 x]=cos (-x)=cos x.
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V PUBLICATION-TRIGNOMETRC FUNCTIONS-QUESTION BANK
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  2. Prove that cos((3pi)/2+x)cos(2pi+x)[cot((3pi)/2-x)+cot(2pi+x)]=1

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  3. Prove that sin(n+1)xsin(n+2)x+cos(n+1)xcos(n+2)x=cosx

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  4. Prove that cos((3pi)/4+x)-cos((3pi)/4-x)=-sqrt2 sinx

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  6. Prove that cos^2 2x-cos^2 6x=sin4x sin8x

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  8. Prove that cot 4 x(sin 5 x+sin 3 x)=cot x(sin 5 x-sin 3 x)

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  12. Prove that (sin x+sin 3 x)/(cos x+cos 3 x)=tan 2 x

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  13. Prove that (sin x-sin 3 x)/(sin ^(2) x-cos ^(2) x)=2 sin x

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