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Choose the correct option and justify your choice : (i) `(2tan30o)/(1+tan^2 30o)=` `(a)"\ "s in"\ "60o\ (b)"\ "cos"\ "60o\ (c)"\ "t a n"\ "60o\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (d)"\ "s in"\ "30o` (ii) `(1-tan^2 45o)/(1+tan^2 45o)=` `(a)"\ "t a

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`(2tan30^(@))/(1+tan^(2)30^(@))= (2xx1/(sqrt(3)))/(1+((1)/(sqrt(3)))^(2))=(2/(sqrt(3)))/(1+(1)/(3))=(2/(sqrt(3)))/(4/(3))=(2)/(sqrt(3))xx(3)/(4)=(sqrt3)/(2)`
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Choose the correct option and justify your choice :(i)(2tan30^(@))/(1+tan^(2)30^(@))(a)sin60^(@)(b)cos60^(@)(c)tan60^(@)(d)sin30^(@)

(2tan30o)/(1+tan^2 30o) is equal to sin60o (b) cos60o (c) tan60o (d) sin30o

(2tan30o)/(1-tan^2 30o) is equal to cos60o (b) sin60o (c) tan60o (d) sin30o

Which among the following is an irrational quantity ? (a) tan 30^(@) tan 60^(@) (b) sin 30 ^(@) (c ) tan 45 ^(@) (d) cos 30^(@)

Evaluate each of the following: (sin^2 45o+cos^2 45o)/(tan^2 60o) (ii) (sin30o-sin90o+2cos0o)/(tan30otan60o)

Verify that: sin60o=(2tan30o)/(1+tan^(2)30o)=(sqrt(3))/(2) (ii) cos60o=(1-tan^(2)30o)/(1+tan^(2)30o)=(1)/(2)

The ratio of the length of a rod and its shadow is 1:sqrt(3) .The angle of elevation of the sum is 30o (b) 45o (c) 60o (d) 90o .

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sin30 ^ (@) sin ^ (2) (60) ^ (@) + 3cos60 ^ (@) tan45 ^ (@) =

NAGEEN PRAKASHAN-INTRODUCTION TO TRIGONOMETRY-Problems From NCERT/exemplar
  1. If angleA and angleB are acute angles such that cos A= cos B, then sho...

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  2. (cos45)/(sec30+cosec30)

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  3. Choose the correct option and justify your choice : (i) (2tan30o)/...

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  4. If tan(A+B)=sqrt(3) and t a n(A B)=1/(sqrt(3)); 0o<A+Blt=90o;""...

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  5. In DeltaA B C , right-angled at B, A B"\ "="\ "5"\ "c m and /A C B=30...

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  6. In P Q R , right-angled at Q ,\ P Q=3c m and P R=6c m . Determine ...

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

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

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

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

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  11. Prove that : 1+(cot^(2)alpha)/(1+"cosec"alpha)="cesec"alpha

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

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

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

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

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

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

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

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

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

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