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If cosx=1/2(a+1/a), show that: cos2x=1/2...

If `cosx=1/2(a+1/a)`, show that:
`cos2x=1/2(a^2+1/a^2)`

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JBD PUBLICATION-TRIGNOMETRIC FUNCTIONS-EXAMPLE
  1. Find sinfrac(x)(2), cosfrac(x)(2) and tanfrac(x)(2) in the following:-...

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  2. Prove the following: (cos4x + cos3x + cos2x)/(sin4x + sin 3x + sin 2x)...

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  3. Show that:(sin11x sinx+sin7x sin3x)/(cos11x sinx + cos7x sin3x)=tan8x

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  4. Prove the following: sin2 x + 2 sin 4x + sin 6x = 4 cos^2 x sin 4x

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  5. Find the general solution for each of the following equations: 2cos^2x...

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  6. Find the general solution for each of the following equations: 4 sin^2...

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  7. Find the general solution of the following equations: sec^2 2x = 1- ta...

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  8. Find the general solution of the following trignometric equations: tan...

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  9. Find the general solution of the following trignometric equations: tan...

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  10. Prove that: (cosx-cosy)^2 +(sinx-siny)^2=4 sin^2frac (x-y)(2)

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  11. If sinx=3/5, cosy=-12/13, where x and y both lie in second quadrant, f...

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  12. Prove that: (cosx-cosy)^2 +(sinx-siny)^2=4 sin^2frac (x-y)(2)

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  13. Show that:sin^2 pi/8 + sin^2 (3pi)/8+sin^2 (5pi)/8+sin^2 (7pi)/8=2

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  14. Show that:[cos((3pi)/4)-cos((2pi)/3)]/[cos((3pi)/4)+cos((2pi)/3)]=3-2s...

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  15. Prove that:cosA.cos(pi/3-A).cos(pi/3+A)=1/4cos3A

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  16. Prove that:tan(x/2)=pmsqrt[(1-cosx)/(1+cosx)]

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  17. Find the value of: cos(pi/8)

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  18. If cosx=1/2(a+1/a), show that: cos2x=1/2(a^2+1/a^2)

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  19. If cosx=1/2(a+1/a), show that: cos3x=1/2(a^3+1/a^3)

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  20. Prove that: cos2x cos(x/2)-cos3x cos((9x)/2)=sin5x sin((5x)/2)

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