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L.H.S. `=(sintheta)/(1+costheta)+(1+costheta)/(sintheta)=(sin^(2)theta+(1+costheta)^(2))/(sintheta(1+costheta))`
`=(sin^(2)theta+(1+2costheta+cos^(2)theta))/(sintheta(1+costheta))`
`=((sin^(2)theta+cos^(2)theta)+1+2costheta)/(sintheta(1+costheta))=(1+1+2costheta)/(sintheta(1+costheta))=(2+2costheta)/(sintheta(1+costheta))`
`=(2(1+costheta))/(sintheta(1+costheta))=(2)/(sintheta)=2"cosec"theta=R.H.S.`
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NAGEEN PRAKASHAN ENGLISH-INTRODUCTION TO TRIGONOMETRY-Problems From NCERT/exemplar
  1. In P Q R , right-angled at Q ,\ P Q=3c m and P R=6c m . Determine ...

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  2. Prove that : sqrt((1-cos^(2)theta)sec^(2)theta)=tantheta

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  3. Prove (tantheta+2)(2tantheta+1)=5tantheta+2sec^2theta.

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  4. If cosA+cos^(2)A=1, then prove that sin^(2)A+sin^(4)A=1.

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

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

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  7. (sinalpha + cosalpha)(tanalpha + cotalpha) = secalpha + cosecalpha

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  8. about to only mathematics

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

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  10. if tantheta+sectheta=l then prove that sectheta=(l^2+1)/(2l)

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  11. If asintheta+bcostheta=c then prove that acostheta-bsintheta=sqrt(a^2+...

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  12. If sintheta+costheta=pandsectheta+"cosec"theta=q then prove that q(p^(...

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  13. Prove that : tantheta+tan(90^(@)-theta)=sectheta*sec(90^(@)-theta)

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  14. Shown that : tan48^(@)tan23^(@)tan42^(@)tan67^(@)=1

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  15. If tan A= cot B. prove that : A+B=90^(@)

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  16. Express sin 67^(@)+cos75^(@) in terms of trigononmertic ratios of angl...

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  17. If tan A=cot (A-18^(@)) where 2A is an acute angle , find the value of...

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  18. If s e c4A=cos e c(A 20o) , where 4A is an acute angle, find the v...

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  19. The value of the expression cosec (75^(@)+theta) - sec(15^@)-theta)-ta...

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  20. If cos(alpha + beta)=0, then sin(alpha-beta) can be reduced to

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