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Show that : (1)/(cos alpha- cos3 alpha...

Show that :
`(1)/(cos alpha- cos3 alpha)+(1)/(cos alpha- cos5 alpha)+(1)/(cos alpha- cos7 alpha)+...+(1)/(cos alpha- cos(2n+1) alpha)=("cosec"alpha)/(2)[ cot alpha- cot (n+1)alpha]`

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1/(cos alpha + cos 3 alpha)+ 1/(cos alpha + cos 5 alpha)+ 1/(cos alpha + cos 7 alpha) +....+ 1/(cos alpha +cos(2n+1) alpha) = 1/2 "cosec" alpha[tan (n+1) alpha - tan alpha ]

Prove that (1)/("cosec"alpha-cot alpha)-(1)/(sin alpha)=(1)/(sin alpha)-(1)/("cosec"alpha+cotalpha) .

Prove that, (cos alpha + sin alpha)/(cos alpha -sin alpha)-(cos alpha - sin alpha)/(cos alpha + sin alpha) = 2 tan 2 alpha

Prove that, (1+ cos 2 alpha + sin 2 alpha)/(1-cos 2 alpha +sin 2 alpha)=cot alpha

Prove that, (sin alpha + cos alpha)/(cos alpha-sin alpha)=tan2 alpha + sec 2 alpha

show that (1-sin^2 alpha)(1-cos^2 alpha)(1+cot^2 alpha)(1+tan^2 alpha) = 1.

Prove that, 1/3 ( cos^(3) alpha sin 3 alpha + sin^(3) alpha cos 3 alpha) = 1/4 sin 4 alpha

Prove that cos alpha cos (120^(@) + alpha) cos (240^(@) + alpha) = 1/4 cos 3 alpha

Prove that cosalpha/(sin3alpha)+(cos3alpha)/(sin9alpha)+(cos9alpha)/(sin27alpha)=1/2[cotalpha-cot27alpha]

CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-TRIGONOMETRY
  1. If (x)/(a) cos theta+(y)/(b) sin theta=1 and x sin theta- y cos theta=...

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  2. If cot x=(a+a^(3)+a^(3))^((1)/(2)), cot y=(1+ a+ a^(-1))^((1)/(2)) and...

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  3. Show that : (1)/(cos alpha- cos3 alpha)+(1)/(cos alpha- cos5 alpha)+...

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  4. If cos alpha=(sin y)/(sinx), cos beta= (sinz)/(sin x) and cos (alpha- ...

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  7. Solve sqrt(2 cos^(2)x+1)+ sqrt(2 sin^(2)x+1)=2 sqrt(2)

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  8. If tan alpha= x tan beta (x gt0), show that tan^(2)(alpha- beta) le ((...

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  9. Prove that cos theta(sin theta +-sqrt(sin^(2) theta+ sin^(2) alpha)) a...

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  10. If cos^(2) theta=(a^(2)-1)/(3) and "tan"^(2) (theta)/(2)= tan^((2)/(3)...

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  12. Prove that cos^(2)40^(@)cos^(2)80^(@)+cos^(2)80^(@)cos^(2)20^(@)+cos^(...

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  13. If x+a= a(2 cos theta-cos 2 theta) and y= a(2 sin theta- sin 2 theta),...

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  14. Show that the value of tan (theta+(pi)/(6)) cot( theta-(pi)/(6)) canno...

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  15. In a triangle of base a, the ratio of the other two sides is r (lt 1)....

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  16. In an acute angled triangle ABC, prove that tan^(2)a+tan^(2)B+tan^(2) ...

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  17. Given sin alpha+ cos alpha+tan alpha+ cot alpha+ sec alpha=7, find th...

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  18. If tan theta= sqrt((a-b)/(a+b))"tan"(A)/(2) and cos varphi =(b+ a cos ...

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  19. Solve : sqrt(tan alphax+ sin x)+ sqrt(tan x-sinx)=2 cos sqrt(tanx)

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