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If cos theta=(7)/(25), " write the valu...

If `cos theta=(7)/(25), " write the value of " (tan theta + cot theta).`

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Verified by Experts

The correct Answer is:
`(625)/(168)`
Consider a right `triangle ABC " in which " angle B =90^(@), AB=7 and AC =25.`
`BC^(2)=AC^(2)-AB^(2)=(25)^(2)-(7)^(2)=(625-49)=576.`
`therefore BC=sqrt(576)=24.`
`therefore (tan theta+cot theta)=((24)/(7)+(7)/(24))=(576+49)/(168)=(625)/(168).`
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RS AGGARWAL-TRIGONOMETRIC IDENTITIES-Exercise 13C
  1. If sin theta=(1)/(2), " write the value of " (3cot^(2)theta+3).

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  2. If cos theta=(2)/(3), " write the value of " (4+ 4 tan^(2)theta).

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  3. If cos theta=(7)/(25), " write the value of " (tan theta + cot theta)...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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