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Prove that: cosec xdotcosec2xdot sin4xdo...

Prove that: `cosec xdotcosec2xdot sin4xdotcos6xdotcos e c 10 x=(cos3x)/(sin2x\ sin4x)+(cos5x)/(sin4x\ sin6x)+(cos7x)/(sin6x\ sin8x)+(cos9x)/(sin8x\ sin10 x)`

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Prove that (cos 3 x)/(sin 2 xsin 4x)+(cos 5x)/(sin 4xsin 6x)+(cos 7x)/(sin 6xsin 8x)+(cos 9x)/(sin 8x sin 10x) =(1)/(2) (co sec x)[co sec2x-co sec 10x]

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ALLEN-TRIGONOMETRIC RATIOS AND IDENTITIES-All Questions
  1. Prove that in an acute angled triangle ABC, the least values of Sigma ...

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  2. In triangle A B C ,\ the est values of sumcos e c(A/2)a n d\ sumsec^2...

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  3. Prove that: cosec xdotcosec2xdot sin4xdotcos6xdotcos e c 10 x=(cos3x)/...

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  4. If t a nalpha=p/q , where alpha=6beta,alpha being acute angle, prove t...

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  5. If tan(pi/4+y/2)=tan^3(pi/4+x/2)dot Prove that (siny)= (sinx)(3+sin^2...

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  6. Q. Prove that from the equality sin^4 alpha/a+cos^4 alpha/b=1/(a+b) fo...

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  7. If P=cos(pi/19)+cos((3pi)/19)+cos((5pi)/19)+....+cos((17pi)/19) and Q=...

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  8. Show that 4sin27^0=(5+sqrt(5))^(1/2)-(3-sqrt(5))^(1/2)

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  9. If A +B+C=pi, prove that tan^(2)""(A)/(2)+tan^(2)""(B)/(2)+tan^(2)""(C...

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  10. If alpha+beta+gamma=pi, prove that : cos^2 alpha + cos^2 beta + cos^2 ...

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  11. In a DeltaABC, if cot A+cot B+cot C=sqrt3. Prove that the triangle is ...

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  12. If the product (sin1^0)(sin3^0)(sin5^0)(sin7^0)....(sin 89^0)=1/(2^n) ...

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  13. For 0ltthetalt pi/2 the solutions(s) of sum(m=1)^6 cosec (theta+ ((m-1...

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  14. If (1+sint)(1+cot t)=(5)/(4) then find the value of (1-sint)(1-cos t).

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  15. tan^(2)'(pi)/(16)+tan^(2)'(2pi)/(16)+tan^(2)'(3pi)/(16)+tan^(2)'(5pi)/...

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  16. Let x1=prod(r=1)^5cos(rpi)/(11)\ a n d\ x2=sum(r=1)^2cos(rpi)/(11), th...

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  17. The period of the function f(x)=sin^(4)x+cos^(4)x is:

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  18. If y=sec^2theta+cos^2theta,\ theta!=0, then- a.y=0 b. ylt=2 c. ygeq-2 ...

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  19. The value of (1-tan^215^0)/(1+tan^215^0)= (A) 1 (B) sqrt(3) (C) sqrt(3...

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  20. If alpha is a root of 25 cos^2theta+5costheta-12=0, pi/2 < alpha < pi,...

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