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( sin(n+1) alpha - sin (n-1)alpha )/( co...

`( sin(n+1) alpha - sin (n-1)alpha )/( cos (n+1) alpha + 2 cos n alpha + cos (n-1) alpha )= `

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cos(n+1) alpha * cos(n-1)alpha + sin (n+1)alpha * sin (n-1) alpha =

(( cos alpha - cos 3 alpha ) ( sin 8 alpha + sin 2 alpha ))/( ( sin 5 alpha - sin alpha ) ( cos 4 alpha - cos 6 alpha ))=

( sin alpha sin 3alpha + sin 3alpha sin 7 alpha + sin 5 alpha sin 15 alpha )/( sin alpha cos 3 alpha + sin 3alpha cos 7 alpha + sin 5 alpha cos 15 alpha ) =

(sin 5 alpha-sin3alpha)/(cos 5 alpha+2 cos 4 alpha+cos 3alpha)=

( cos 2 alpha)/( cos^(4) alpha - sin^(4) alpha ) -(cos^(4) alpha + sin^(4) alpha )/(2-sin^(2) 2alpha ) =

sin^(2) alpha * tan alpha + cos^(2) alpha * cot alpha + 2 sin alpha cos alpha =

( sin 8 alpha * cos alpha - sin 6 alpha * cos 3 alpha )/(cos 2 alpha cos alpha - sin 3 alpha * sin 4alpha ) =

If (sin alpha )/(a) = ( cos alpha )/(b) , then a sin 2alpha + b cos 2 alpha =

I : If (cos alpha )/(a)=(sin alpha )/(b) then a cos 2 alpha + b cos 2 alpha =a II : If (sin alpha )/(a) =(cos alpha )/(b) then a sin 2 alpha + b cos 2 alpha = a

VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-TRIGONOMETRIC RATIOS UPTO TRANSFORMATIONS-EXERCISE - 6(E)
  1. Prove that sin50^(@)-sin70^(@)+sin10^(@)=0

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  2. Prove that (sin70^(@)-cos40^(@))/(cos50^(@)-sin20^(@)) = 1/(sqrt(3)).

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  3. cos 55^circ + cos 65^circ +cos175^circ =0అని రుజువు చేయండి.

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  4. Prove that 4(cos66^(@)+sin84^(@)) = sqrt(3) + sqrt(15).

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  5. Prove that cos20^(@)cos40^(@)-sin5^(@)sin25^(@)=(sqrt(3)+1)/4

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  6. Prove that cos48^@.cos12^@=(3+sqrt5)/8.

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  7. Prove that cos theta + cos[(2pi)/3 + theta] + cos [(4pi)/(3) + theta] ...

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  8. If sin x+siny=1/4,cos x+cosy=1/3 then tan((x+y)/2)=

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  9. sin x + sin y = 1/4, cos x+ cos y = 1/3అయిలే ii) cot(x +y) = 7/24 అని ...

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  10. Prove that 4cos12^(@)cos48^(@)cos72^(@)=cos36^(@).

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  11. sin10^(@)+sin20^(@)+sin40^(@)+sin50^(@)-sin70^(@)-sin80^(@)=

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  12. If cos x+ cosy =(4)/(5) and cos x- cos y =(2)/(7), then the value of 1...

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  13. If none of the denominators is zero, prove that. ((cosA+cosB)/(sinA-...

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  14. If sinA=sinBandcoA=cosB then A =

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  15. ( sin(n+1) alpha - sin (n-1)alpha )/( cos (n+1) alpha + 2 cos n alpha ...

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  16. If sec(theta+alpha)+sec(theta-alpha)=2sec theta and cos alpha!=1, prov...

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  17. If sin (y+z-x), sin (z+x-y), sin (x+y-z) are in A. P , then prove that...

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  18. If x,y,z are non zero real numbers and if x cos theta=y cos (theta+(2p...

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  19. If m sin B= n sin (2A+B) then show that (m+n)tanA=(m-n)tan(A+B)

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  20. tan(A +B) = lambda tan(A-B) అయితే (lambda +1) sin 2B =(lambda -1)sin2A...

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