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If A+B+C=pi, then prove the following. ...

If `A+B+C=pi`, then prove the following.
`cos^2A+cos^2B+2cosA cdot cosB cdot cos C=sin^2 C`

Text Solution

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`cos^2A+cos^2B+cos^2C`
`=(1+cos2A)/2+(1+cos2B)/2+(1+cos2C)/2
`(3+cos2A+cos2B+cos2C)/2`
`=(3-1-4cosAcosBcosC)/2`
`=(2-4cosAcosBcosC)/2`
`1-2cosAcosBcosC`
or, `cos^2A+cos^2B+2cosAcosBcosC`
`=1-cos^2C=sin^2C`
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MBD PUBLICATION-TRIGONOMETRIC FUNCTIONS-QUESTION BANK
  1. If A+B+C=pi, then prove the following. cosA+cosB+cosC=1+4sinfrac{1}{...

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  2. If A+B+C=pi, then prove the following. sinA+sinB-sinC=4sinfrac{1}{2}...

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  3. If A+B+C=pi, then prove the following. cos^2A+cos^2B+2cosA cdot cosB...

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  4. If A+B+C=pi, then prove the following. sin^2frac{A}{2}+sin^2frac{B}{...

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  5. If A+B+C=pi, then prove the following. sinfrac{A}{2}+sin frac{B}{2}+...

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  6. If A+B+C=pi, then prove the following. cos^2frac{A}{2}+cos^2frac{B}{...

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  7. If A+B+C=pi, then prove the following. sin(B+2C)+sin(C+2A)+sin(A+2B)...

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  8. Show that (2costheta-1) (2cos2theta-1) (2cos2^2theta-1)……(2cos2^(n-1)t...

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  9. Show that 2^ncostheta cdot cos2thetacdotcos2^2theta......cos2^(n-1)t...

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  10. Prove that tan2^ntheta/(tantheta) =(1+sec2theta)(1+sec2^2theta)....(1+...

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  11. If x+y+z=xyz, prove that x/(1-x^2)+ y/(1-y^2)+z/(1-z^2) =(4xyz)/((1-x...

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  12. If x+y+z=xyz, prove that (3x-x^3)/(1-3x^2)+(3y-y^3)/(1-3y^2)+(3z-z^3)/...

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  13. Ifsin^4alpha/a+cos^4alpha/b=1/(a+b) show that sin^8alpha/a^3+cos^8alph...

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  14. The number of solutions of 2sintheta-1=0 is.

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  15. If cosalpha=cosbeta, then alpha+beta=

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  16. The number of solution(s) of 2sectheta+1=0 is.

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  17. If tantheta=tanalpha and 90ltalphalt180, then ' theta ' can be in th...

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  18. If tanx cdot tan 2x cdot tan 7x =tanx+tan2x+tan7x, then x=

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  19. For value of theta, sintheta+costheta=sqrt2

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  20. The number of values of x for which cos^2x=1 and x^2le 4 is

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