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Show that 1+cot^2alpha/(1+cosecalpha)=co...

Show that `1+cot^2alpha/(1+cosecalpha)=cosec alpha`

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LHS = `1+ (cot^(2)alpha)/(1+"cosec"alpha)=1+(cos^(2)alpha//sin^(2)alpha)/(1+1//sinalpha)` `[therefore cottheta=(costheta)/(sintheta)` and `"cosec"theta=1/(sintheta)]`
`=1+ (cos^(2)alpha)/(sinalpha(1+sin alpha))`
`=(sinalpha + 1)/(sinalpha(sinalpha+1))=1/sinalpha` `[therefore "cosec"theta=1/sintheta]`
`="cosec"alpha=RHS`
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NCERT EXEMPLAR-INTRODUCTION TO TRIGoNOMETRY AND ITS APPLICATIONS-Introduction To Trigonometry And Its Applications
  1. (sinalpha + cosalpha)(tanalpha + cotalpha) = secalpha + cosecalpha

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  2. Prove that (sqrt(3)+1)(3-cot30^@)=tan^3(60)^@-2sin60^@

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  3. Show that 1+cot^2alpha/(1+cosecalpha)=cosec alpha

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  4. tantheta+tan(9 0^(@)-theta)=secthetaxxsec(9 0^(@)-theta)

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  5. Find the angle of elevation of the Sun when the shadow of a pole h m ...

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  6. If sqrt(3)tantheta=1 then find value of sin^2theta-cos^2theta

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  7. A ladder 15 m long just reaches the top of a vertical wall. If the ...

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  8. Simplify: (1+tan^(2)theta)(1-sintheta)(1+sintheta)

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  9. If 2sin^2theta-cos^2theta=2, find the value of theta.

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  10. Evaluate : (cos^2(45 + theta) + cos^2(45 - theta))/(tan(60^@ + theta)...

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  11. An observer, 1.5 m tall, is 20.5 m away from a tower 22 m high. Determ...

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  12. Prove the following identity: sec^4theta-sec^2theta=tan^4theta+tan^2th...

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  13. If cosectheta + cottheta=p, then cos theta=

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  14. Prove that sqrt(sec^(2)theta + cosec^(2)theta) = tantheta + cottheta.

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  15. The angle of elevation of the top of a tower from a certain point is 3...

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  16. If 1+sin^(2)theta = 3sinthetacostheta, then prove that tantheta=1 or 1...

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  17. If sintheta + 2 costheta=1,then 2sintheta-costheta=

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  18. The angle of elevation of the top of a tower from two distinct points ...

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  19. The shadow of a tower standing on a level ground is found to be 40 m ...

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  20. A vertical tower Stands on a horizontal plane and is surmounted by a v...

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