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Prove that (cos(pi+x)cos(-x))/(sin(pi-x)...

Prove that `(cos(pi+x)cos(-x))/(sin(pi-x)cos(pi/2+x)`=`cot^2x`

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V PUBLICATION-TRIGNOMETRC FUNCTIONS-QUESTION BANK
  1. Prove that cos(pi/4-x)cos(pi/4-y)-sin(pi/4-x)sin(pi/4-y)=sin(x+y)

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  2. prove that (tan(pi/4+x))/(tan(pi/4-x))=((1+tanx)/(1-tanx))^2

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  3. Prove that (cos(pi+x)cos(-x))/(sin(pi-x)cos(pi/2+x)=cot^2x

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  4. Prove that cos((3pi)/2+x)cos(2pi+x)[cot((3pi)/2-x)+cot(2pi+x)]=1

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

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

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  7. prove the following sin^2 6x-sin^2 4x =sin2xsin10x

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

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  9. Prove that sin 2 x+2 sin 4 x+sin 6 x=4 cos ^(2) x sin 4 x

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

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  11. Prove that (cos 9 x-cos 5 x)/(sin 17 x-sin 3 x)=-(sin 2 x)/(cos 10 x...

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  12. Prove that (sin 5 x+sin 3 x)/(cos 5 x+cos 3 x)=tan 4 x

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  13. Prove that (sinx-siny)/(cosx+cosy)=tan(x-y)/2

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

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

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  16. Prove that (cos 4 x+cos 3 x+cos 2 x)/(sin 4 x+sin 3 x+sin 2 x)=cot 3 x...

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  17. Prove that cot x cot 2 x-cot 2 x cot 3 x-cot 3 x cot x=1

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  18. Prove that tan4x=(4tanx(1-tan^2x))/(1-6tan^2x+tan^4x)

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  19. Prove that cos 4(x)=1-8 sin ^(2) (x) cos ^(2) (x)

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  20. Prove that cos 6 x=32 cos ^(6) x-48 cos ^(4) x+18 cos ^(2) x-1

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