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If alpha, beta, gamma ,are positive acut...

If `alpha, beta, gamma` ,are positive acute angles and `sin (alpha+beta-gamma)=cos(beta+gamma-alpha)=tan (gamma+alpha-beta)=1` find `alpha,beta and gamma` .

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The correct Answer is:
`alpha=67.5^@, beta=45^@, gamma=22.5^@`
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CHHAYA PUBLICATION-TRIGONOMETRIC RATIOS [OR FUNCTIONS] OF POSITIVE ACUTE ANGLES-EXERCISE 2
  1. Solve : (0^@le thetale90^@): 2 sin ^2theta=3(1-cos theta)

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  2. Solve : (0^@le thetale90^@): 2 sin theta tan theta +1=tan theta+2 s...

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  3. If alpha, beta, gamma ,are positive acute angles and sin (alpha+beta-g...

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  4. If A,B,C are the angles of an acute angled triangle and cos(B+C-A)=0, ...

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  5. If 1+cos^2A=3 cos AsinA, find the value of cotA.

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  6. If 3 sin theta+4cos theta=5(0lt theta lt pi/2), show that sin theta =3...

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  7. If cosecalpha+cotalpha=a, prove that , cos alpha =(a^2-1)/(a^2+1).

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  8. If 4xsec A =1+4x^2 , prove that, sec A +tan A=2xor,1/(2x).

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  9. If tan ^2theta=1-e^2 , prove that, sectheta+tan^3thetacosec theta=(2-e...

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  10. If a^2sec^2alpha-b^2tan^2alpha=c^2 show that, sinalpha=pm sqrt((c^2-a^...

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  11. If sin^4theta+sin^2 theta=1 show that, tan^4theta-tan^2theta=1 .

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  12. If tan^4theta+tan^2theta=1 , prove that, cos^4 theta+cos^2theta=1

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  13. If sin^2theta=cos^3theta prove that, cot^6theta-cot^2theta=1 .

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  14. If sin theta+sin^2theta=1 , show that cos^4theta+cos^2theta=1.

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  15. If cos theta -sin theta =sqrt(2) sin theta , show that, costheta+sinth...

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  16. If un=sin ^n alpha+cos^nalpha then show that, the value of 6u4-4u6 is...

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  17. Find the principal value of cos^-1(-1/2)

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  18. Eliminate theta in each of the following : x=asec theta, y=btan the...

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  19. Eliminate theta in each of the following : a sin theta=p, btan the...

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  20. Eliminate theta in each of the following : sin theta+cos theta=m, t...

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