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If cottheta=1/(sqrt(3)) , show that (...

If `cottheta=1/(sqrt(3))` , show that `(1-cos^2theta)/(2-sin^2theta)=3/5`

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Verified by Experts

The correct Answer is:
`(3)/(5)`
`((1-cos^(2)theta))/((2-sin^(2)theta))=(sin^(2)theta)/((2-sin^(2)theta))=((3)/(4))/((2-(3)/(4)))" "["cosec"^(2)theta=(1+cot^(2)theta)=(1+(1)/(3))=(4)/(3) rArr sin^(2)theta=(3)/(4)]`
`=((3)/(4)xx(4)/(5))=(3)/(5).`
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RS AGGARWAL-TRIGONOMETRIC IDENTITIES-Exercise 13C
  1. If 5 tan theta =4, " write the value of " ((costheta- sintheta ))/((c...

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  2. If 3 cot theta =4, " write the value of " ((2costheta+ sintheta ))...

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  3. If cottheta=1/(sqrt(3)) , show that (1-cos^2theta)/(2-sin^2theta)=3...

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  4. If tan theta =(1)/(sqrt(5)), " write the value of " (("cosec"^(2)th...

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  5. If cot A =(4)/(3) and (A+B)=90^(@), what is the value of tan B?

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  6. If A+B=90o and cosB=3/5 , what is the value of sinA ?

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  7. If sqrt(3) sin theta = cos theta and theta" is an acute angle, find ...

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  8. The value of tan 10^(@)* tan20^(@)*tan45^(@)*tan70^(@)*tan80^(@)=

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  9. The value of tan1^@ tan 2^@ tan 3^@ ... tan 89^@ is

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  10. Write the value of cos 1^(@) cos 2^(@) … cos 180^(@).

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  11. If tan A=5/12, find the value of (sin A+cos A) sec A

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  12. If sin theta = cos (theta - 45^(@)), " where " theta " is acute, fin...

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  13. Find the value of (sin 50^(@))/(cos40^(@))+("cosec"40^(@))/(sec 50...

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  14. Find the value of sin 48^(@) sec 42^(@)+cos48^(@) "cosec"42^(@).

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  15. If x=a sin theta and y = b cos theta , " write the value of " (b^(2)x...

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  16. If 5x=sectheta and 5/x=tantheta , find the value of 5(x^2-1/(x^2)) ...

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  17. If cos e c\ theta=2x and cottheta=2/x , find the value of 2(x^2-1/(...

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  18. If sec theta + tan theta =x, " find the value of " sec theta.

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  19. Choose the correct answer in each of the following questions: (cos38...

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  20. If sin theta =x, " write the value of " cot theta.

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