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Evaluate: (cos45)/(sec30+cosec30)...

Evaluate:
`(cos45)/(sec30+cosec30)`

Text Solution

Verified by Experts

`(cos45^(@))/(sec30^(@)+"cosec"30^(@))=(cos45^(@))/(sec30^(@)+"cosec"30^(@))=(1/(sqrt(2)))/(2/sqrt(3)+2)=(1/(sqrt(2)))/(((2+2sqrt(3)))/(sqrt(3)))`
`=(1)/(sqrt(2))xx(sqrt(3))/(2(sqrt(3)+1))= (sqrt(3)(sqrt(3)-1))/(2sqrt(2)(sqrt(3)+1)(sqrt(3)-1))`
`=(sqrt(6)(sqrt(3)-1))/(4(3-1))=(sqrt(6)(sqrt(3)-1))/(8)`
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NAGEEN PRAKASHAN ENGLISH-INTRODUCTION TO TRIGONOMETRY-Problems From NCERT/exemplar
  1. If s in A=3/4 , calculate cos A and tan A.

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  2. If /Aand /Bare acute angles such that cos A=cos B. then show that /A=...

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  3. Evaluate: (cos45)/(sec30+cosec30)

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  4. solve : (2tan30^@)/(1+tan^2 30^@)

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

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

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

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

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

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

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

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

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

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  14. about to only mathematics

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

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

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

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

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

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

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