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Show that tan1^0tan2^0tan89^0=1...

Show that `tan1^0tan2^0tan89^0=1`

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`L.H.S.=(tan1^@tan89^@)(tan2^@tan88^@)…`
`(tan44^@tan46^@)tan45^@`
`=[tan1^@tan(90^@-1^@)][tan2^@tan(90^@-2^@)]…`
`[tan44^@tan(90^@-44^@)]tan45^@`
`=(tan1^@cot1^@)(tan2^@cot2^@)…`
`(tan44^@cot44^@)tan45^@=1`
`[ :'tanthetacottheta" and " tan45^@=1]`
=R.H.S.
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CENGAGE ENGLISH-TRIGONOMETRIC FUNCTIONS -SINGLE CORRECT ANSWER TYPE
  1. Show that tan1^0tan2^0tan89^0=1

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  2. The circular wire of diameter 10 cm is cut and placed along the circum...

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  3. about to only mathematics

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  4. If theta in (pi//4, pi//2) and sum(n=1)^(oo)(1)/(tan^(n)theta)=sin the...

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  6. If 15 sin^(4)alpha+10cos^(4)alpha=6, then the value of 8 cosec^(6)alph...

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  8. If (sin^(2)x-2cos^(2)x+1)/(sin^(2)x+2cos^(2)x-1)=4, then the value of ...

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  9. If sintheta,tantheta,costheta are in G.P. then 4sin^2theta-3sin^4theta...

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  10. If tantheta-cottheta=aandsintheta+costheta=b, then, (b^2-1)^2(a^2+4...

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  11. The least value of 18 sin^(2)theta+2 cosec^(2)theta-3 is (a) -15 (b) ...

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  12. If tan^2 alpha tan^2 beta + tan^2 beta tan^2 gamma + tan^2 gamma tan^2...

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  15. If (cos alpha)/(cos A)+(sin alpha)/(sin A)+(sin beta)/(sin A)=1, where...

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  16. Consider angles alpha = (2n+(1)/(2))pi pm A and beta = m pi +(-1)^(m)(...

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  17. Which of the following is true ?

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  18. If the angle A of a triangle ABC is given by the equation 5 cos A + 3 ...

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  19. Which of the following is greatest ?

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  21. Which of the following is not correct ?

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