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If sinx=4/5 and 0ltxltpi/ 2, find the v...

If `sinx=4/5` and `0ltxltpi/ 2,` find the value of `sin4x`

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Verified by Experts

Given, `sinx=4/5`
So,
`=>cosx=sqrt(1-sin^2x)`
`=>cosx=sqrt(1-(16)/(25))`
`=>cosx=sqrt(9/(25))`
`=>cosx=3/5`
so,
...
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RD SHARMA-TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES-Solved Examples And Exercises
  1. Prove that 1+cos^2 2x=2(cos^4x+sin^4x)

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  2. If costheta=4/5 and theta is acute, find the tan2theta

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  3. If sinx=4/5 and 0ltxltpi/ 2, find the value of sin4x

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  4. Prove that: \ cos7^0cos 14^0cos 28^0cos 56^0=(s in 68^0)/(16cos83^0)

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  5. Prove that: cos(pi/5)cos((2pi)/5)cos((4pi)/5)cos((8pi)/5)=(-1)/16

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  6. cos((2pi)/65)cos((4pi)/65)cos((8pi)/65)cos((16pi)/65)=1/16

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  7. If 2\ t a nalpha=3t a nbeta, prove that tan(alpha-beta)=(sin2beta)/(5...

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  8. sinalpha+sinbeta=a ,cosalpha+cosbeta=b=>sin(alpha+beta)

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  9. If sinalpha+sinbeta=a and cosalpha+cosbeta=b prove that: cos(alpha-bet...

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  10. If costheta=(cosalpha+cosbeta)/(1+cosalphacosbeta),\ prove that tanth...

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  11. If sec(theta+alpha)+sec(theta-alpha)=2\ s e ctheta, prove that costhet...

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  12. If cos alpha=4/5 and cos beta =5/13, prove that cos (alpha-beta)=56/65

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  13. Prove that: 8cos^3pi/9-\ 6cospi/9=1.

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  14. Prove that: 108sinpi/(18)-144sin^3pi/(18)=18

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  15. Prove that cos6x=32cos^6x-48cos^4x+18cos^2x-1

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  16. Prove that : cos Acos(60-A)cos(60+A)=1/4cos3A

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  17. Prove that: sin A sin(60-A)sin(60+A)=1/4sin3Adot

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  18. Prove that: "sin"20^0"sin"40^0"sin"60^0"sin"80^0=3/(16)

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  19. prove sin(5theta) = 16sin^5(theta)-20sin^3(theta)+5sin(theta)

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  20. Prove the following identity: 4(cos^3 10^0+sin^3\ \ 20^0)=\ 3\ (cos 10...

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