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If u(n)=2 cos n theta, then show that u(...

If `u_(n)=2 cos n theta`, then show that `u_(n+1)= u_(1)u_(n)-u_(n-1)`, hence, show that `2 cos 5 theta= u_(1)^(5)- 5u_(1)^(3)+ 5u_(1)`

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CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-TRIGONOMETRY
  1. If tan (pi cot theta )= cot (pi tan theta), then show that tan theta= ...

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  2. If tan (pi cos theta)= cot (pi sin theta), show that cos (theta-(pi)/(...

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  3. If u(n)=2 cos n theta, then show that u(n+1)= u(1)u(n)-u(n-1), hence, ...

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  4. Show that the value of (cot 3x)/(cot x) cannot lie between (1)/(3) an...

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  5. If (sin theta + cos theta )=sqrt(2) cos theta , show that cot theta =...

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  6. Show that 3(sin x- cos x)^(4)+4 (sin ^(6)x+cos^(6)x)+ 6(sin x+cos x)^(...

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  7. Show that 1+cos 56^(@)+ cos 58^(@)-cos66^(@)=4 cos 28^(@) cos 29^(@...

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  8. If alpha= (2pi)/(7), then prove that cos alpha+ cos 2 alpha+ cos 4alph...

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  9. In any triangle ABC if sin A sin B sin C+ cos A cos B=1, then show tha...

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  10. If sin theta+ sin phi= sqrt(3)( cos phi- cos theta), then show that si...

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  11. Prove that : tan 70^(@)+ tan 10^(@)- tan 50^(@)= sqrt(3)

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  12. Prove that : 4 sin 50^(@)- sqrt(3) tan 50^(@)=1

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  13. If alpha, beta , gamma lengths of the altitudes of a triangle ABC, pro...

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  14. If a sin theta+ b cos theta=0,then find theta

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  15. If cos^(3) theta = kcos (alpha- 3 theta) and sin ^(3) theta= ksin (alp...

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  16. Show that the general solution of sin x- 3 sin 2x+sin 3x= cos x-3 cos ...

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

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

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

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

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