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If 5 tan theta =4, " write the value of...

If `5 tan theta =4, " write the value of " ((costheta- sintheta ))/((costheta+ sintheta)).`

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The correct Answer is:
`(1)/(9)`
`((costheta-sintheta))/((costheta+sintheta ))=((1-tantheta))/((1+tantheta))" "["dividing num. denom. by cos"theta]`
`=((1-(4)/(5)))/((1+(4)/(5)))=(1)/(9) " "[because tantheta=(4)/(5)].`
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RS AGGARWAL-TRIGONOMETRIC IDENTITIES-Exercise 13C
  1. If cos theta=(7)/(25), " write the value of " (tan theta + cot theta)...

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  2. If cos theta = (2)/(3), " write the value of " ((sectheta-1))/((secth...

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  3. If 5 tan theta =4, " write the value of " ((costheta- sintheta ))/((c...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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