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If k is a positive integer, show that ...

If k is a positive integer, show that
`2[ cos x+ cos 3x+ cos 5x+ ..+ cos (2k-1)x] = (sin 2kx)/(sin x)`

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CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-TRIGONOMETRY
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  2. Show that the general solution of sin x- 3 sin 2x+sin 3x= cos x-3 cos ...

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  3. If k is a positive integer, show that 2[ cos x+ cos 3x+ cos 5x+ ..+ ...

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  4. If alpha=(pi)/(8 n) then prove that sin^(2) alpha+ sin^(2)3 alpha+ sin...

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  5. If sin A+ tan A= a and cos A+ cot A= b, then show that (1+a)^(-2)+(1...

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  6. If a^(2)(1- sin theta) +b^(2)(1+ sin theta)= 2 ab cos theta then show ...

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  7. Show that (1+ sin A)/(cosA)+( cos B)/(1- sin B)=(2 (sin A- sin B))/(...

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  8. If n is positive integer and "cos" (pi)/(2n)+"sin" (pi)/(2n) =(sqrt(n)...

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  9. Solve : sec theta+"cosec" theta=2 sqrt(2)

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  10. Solve : tan^(3) theta+ cot^(3) theta= 8 "cosec"^(3) 2 theta+12

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  11. Solve : ("sin" (x)/(2) "cos" (x)/(2))/(1-8 "sin"^(2)(x)/(2) "cos"^(2...

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  12. Solve : cos theta cos 2 theta cos 3 theta =(1)/(4) (0 le theta le p...

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  13. If cos beta is the geometric mean of sin alpha and cos alpha, then sho...

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  14. Prove that "sin" (pi)/(14)"sin" (3pi)/(14) "sin" (5pi)/(14) "sin" (7p...

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  15. The sides of a triangles are in A.P.and the greatest angle exceeds the...

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  16. Let 0 lt x lt pi, 0 lt y lt pi and cos x+ cos y - cos (x+y)=(3)/(2). ...

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  17. Eliminate x and y from the following equations : a sin ^(2)+ b cos^(2)...

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  18. Find the root of equation 2x^2+3 x + 11=0.

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  19. If a cos theta+ b sin theta= c then find the quadratic equation whose...

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  20. If alpha=(2pi)/(7) then prove that sin alpha sin 2 sin 4 alpha =-(sqrt...

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