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Eliminate theta each of the following : ...

Eliminate `theta` each of the following :
`l_1cos theta+m_1sin theta+n_1=0,l_2cos theta+m_2sin theta+n_2=0`

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The correct Answer is:
`(m_1n_2-m_2n_1)^2+(n_1l_2-n_2l_1)^2=(l_1m_2-l_2m_1)^2`
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CHHAYA PUBLICATION-TRIGONOMETRIC RATIOS [OR FUNCTIONS] OF POSITIVE ACUTE ANGLES-EXERCISE 2
  1. Eliminate theta in each of the following : sintheta -cos theta=a, ...

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

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

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

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

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

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

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

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

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

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

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

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

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  14. Prove that cos^2A-sin^2A = (1-tan^2A)/(1+tan^2A).

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  15. If a sin x =bcos x=(2ctanx)/(1-tan^2x), prove that, (a^2-b^2)^2=4c^2(a...

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  16. If costheta =(cosalphacosbeta)/(1+sin alpha sin beta), show that , sin...

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  17. If (cos^4x)/(cos^2y)+(sin^4x)/(sin^2y)=1,"show taht", (cos^4y)/(cos^2x...

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  18. If cosec x =cosec y cosec z+cot y cot z, prove that cosec y=cosec z co...

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  19. If (xcos theta)/a+(ysin theta)/b=1 and (ax)/(cos theta)-(by)/(sin thet...

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  20. Find the principal value of tan^-1(-1/sqrt3)

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