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Let p(k)=(1+cos((pi)/(4k)))(1+cos((2k-1)...

Let `p(k)=(1+cos((pi)/(4k)))(1+cos((2k-1)pi)/(4k))`
`(1+cos""((2k+1)pi)/(4k))(1+cos""((4k-1)pi)/(4k))`, then

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Let P(k)=(1+cos(pi/(4k))) (1+cos(((2k-1)pi)/(4k))) (1+cos(((2k+1)pi)/(4k)))(1+cos(((4k-1)pi)/(4k)))dot Then Prove that (a) P(3)=1/(16) (b) P(4)=(2-sqrt(2))/(16) (c) P(5)=(3-sqrt(5))/(32) (d) P(6)(2-sqrt(3))/(16)

Let P(k)=(1+cospi/(4k)) (1+cos((2k-1)pi)/(4k)) (1+cos((2k+1)pi)/(4k))(1+cos((4k-1)pi)/(4k))dotT h e n P(3)=1/(16) (b) P(4)=(2-sqrt(2))/(16) P(5)=(3-sqrt(5))/(32) (d) P(6)(2-sqrt(3))/(16)

Let P(k)=(1+cospi/(4k)) (1+cos((2k-1)pi)/(4k)) (1+cos((2k+1)pi)/(4k))(1+cos((4k-1)pi)/(4k))dotT h e n P(3)=1/(16) (b) P(4)=(2-sqrt(2))/(16) P(5)=(3-sqrt(5))/(32) (d) P(6)(2-sqrt(3))/(16)

Let F(x)=(1+sin(pi/(2k))(1+sin(k-1)pi/(2k))(1+sin(2k+1)pi/(2k))(1+sin(3k-1)pi/(2k)) . The value of F(1)+F(2)+F(3) is equal to

prod_(k=0)^3 (1+cos\ ((2k+1)pi)/8)=

tan((pi)/(4) +(1)/(2)"cos"^(-1)(a)/(b))+ tan((pi)/(4) - (1)/(2)"cos"^(-1)(a)/(b)) is :

If cosec . (pi)/(32)+ cosec. (pi)/(16)+ cosec. (pi)/(8)+ cosec. (pi)/(4)+ cosec. (pi)/(2)= cot. (pi)/(k) , then the value of k is

The value of 1+sum_(k=0)^(14) {cos((2k+1)pi)/(15) - isin((2k+1)pi)/(15)} , is

The value of sum_(k=1)^(3) cos^(2)(2k-1)(pi)/(12), is

"cos(pi/15)cos((2pi)/15)cos((4pi)/15)cos((8pi)/15)=k

ALLEN-TRIGONOMETRIC RATIOS AND IDENTITIES-All Questions
  1. If the value of the expression sin 25^@* sin 35^@* sin 85^@ can be exp...

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  2. Prove that (4cos^2 9^0-3)(4cos^2 27^0-3)=tan9^0dot

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  3. Let p(k)=(1+cos((pi)/(4k)))(1+cos((2k-1)pi)/(4k)) (1+cos""((2k+1)pi)...

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  4. If (1+t a n1^0). (1+t a n2^0) .(1+t a n3^0)......(1+tan45^0)=2^n , the...

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  5. Prove that in an acute angled triangle ABC, the least values of Sigma ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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