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If un=sin ^n alpha+cos^nalpha then show ...

If `u_n=sin ^n alpha+cos^nalpha` then show that, the value of `6u_4-4u_6` is independent of `alpha` .

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CHHAYA PUBLICATION-TRIGONOMETRIC RATIOS [OR FUNCTIONS] OF POSITIVE ACUTE ANGLES-EXERCISE 2
  1. If sin theta+sin^2theta=1 , show that cos^4theta+cos^2theta=1.

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

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

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

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

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

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

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  8. Eliminate theta in each of the following : sintheta -cos theta=a, ...

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  9. If 7sin ^2theta +3cos^2theta =4, prove that, tan theta =pm1/sqrt(3) .

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  10. Find the minimum value of cos^4 theta+sin^2 theta.

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  11. If p tan theta=tan p theta , show that, (sin^2p theta)/(sin^2theta)=(p...

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  12. If (1+sin alpha)(1+sinbeta)(1+singamma)=(1-sinalpha)(1-sinbeta)(1-sing...

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  13. If (cosecalpha-1)(cosecbeta-1)(cosecgamma-1)=(cosecalpha+1)(cosecbeta+...

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  14. Eliminate theta each of the following : l1cos theta+m1sin theta+n1=0...

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  15. Eliminate theta each of the following : asec theta +btan theta+c=0,...

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  16. Eliminate theta each of the following : cos^3 theta +3costhetasin^2...

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  17. If tan theta+sin theta=m and tan theta-sin theta=n, prove that, mn=tan...

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  18. If "cosec" theta- sin theta=m^(3) and sec theta-cos theta=n^(3), then ...

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  19. If (sin^4theta)/x+(cos^4theta)/y=1/(x+y), show that ,(sin^(2m+2)theta)...

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  20. If cosec alpha+cot alpha=2+sqrt(5) , show that, cosalpha=2/sqrt(5).

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