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Prove that cos 2 x cos (x/2)-cos 3 x co...

Prove that `cos 2 x cos (x/2)-cos 3 x cos ((9x)/2)=sin 5 x sin ((5 x)/2)`

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V PUBLICATION-TRIGNOMETRC FUNCTIONS-QUESTION BANK
  1. Find the principal and general solution of the following equation sin ...

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  2. If sin x=(3)/(5), cos y=-(12)/(13), where 'x' and 'y' both lie in seco...

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

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  4. Find the value of tan (pi/8)

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  5. If tan x^(circ)=(3)/(4), piltxlt(3 pi)/(2), find the value of sin (x)...

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  6. Show that cos ^(2) x+cos ^(2)(x+(pi)/(3))+cos ^(2) (x-(pi)/(3))=(3)/(2...

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  7. Prove that 2cos(pi/13)cos((9pi)/13)+cos((3pi)/13)+cos((5pi)/13)=0

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  8. Prove that (sin 3 x+sin x) sin x+(cos 3 x-cos x)cosx=0

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  9. Prove that (cosx+cosy)^2+(sinx-siny)^2=4cos^2((x+y)/2)

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  10. Prove that (cos x-cos y)^(2)+(sin x-sin y)^(2)=4 sin ^(2)((x-y)/(2))

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

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  12. Prove that ((sin 7 x+sin 5 x)+(sin 9 x+sin 3 x))/((cos 7 x+cos 5 x)+(c...

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  13. Show that sin 3 x+sin 2 x-sin x=4 sin x cos (x/2) cos ((3 x)/2)

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  14. Find sin(x/2) , cos(x/2) , and tan(x/2) if tanx=-4/3 and x is in the s...

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  15. Find sin(x/2) , cos(x/2) and tan(x/2) if cosx=(-1/3) and x lies in the...

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  16. Find sin(x/2), cos(x/2) and tan(x/2) if sinx=1/4 and x lies in the sec...

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  17. Prove that (sin x)/(1+cos x)=tan (x/2) Find the domain and range of f(...

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  18. Hence write the value of cos 75^@.

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  19. If (sin (x+y))/(sin (x-y))=(a+b)/(a-b), show that a tan y=b tan x

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  20. Prove that cos 24^(circ)+cos 55^(circ)+cos 125^(circ)+cos 204^(circ)+...

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