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Prove the following identity: sec^4theta...

Prove the following identity: `sec^4theta-sec^2theta=tan^4theta+tan^2theta`

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L.H.S. `=tan^(4)theta+tan^(2)theta=tan^(2)theta(tan^(2)theta+1)`
`=(sec^(2)theta-1)sec^(2)theta=sec^(4)theta-sec^(2)theta=R.H.S.`
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NAGEEN PRAKASHAN-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. Prove that : 1+(cot^(2)alpha)/(1+"cosec"alpha)="cesec"alpha

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  7. Prove that : (sinalpha+cosalpha)(tanalpha+cotalpha)=secalpha+"cosecα...

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  8. Prove that : (sintheta)/(1+costheta)+(1+costheta)/(sintheta)=2"cosec"t...

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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 tantheta=(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+tantheta+tan(90^(@)-theta)=sectheta*sec(90^(@)-t...

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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 sec4A ="cosec"(A-20^@) where 4A is an acute angle , find the value ...

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

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

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