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Prove the following results: tan(cos^(...

Prove the following results: `tan(cos^(-1)""4/5+tan^(-1)""2/3)=(17)/6`
(ii) `cos(sin^(-1)""3/5+cot^(-1)""3/2)=6/(5sqrt(13))`

Text Solution

Verified by Experts

Let `sin^(-1)3/5=theta`, Then,`sin theta=3/5`.
Draw a right triangle in which
perp. =3 units,
hyp. =5units and
base `=sqrt((5)^(2)-(3)^(2))=sqrt(16)=4` units.

`therefore tantheta=3/4 rArr theta=tan^(-1)3/4`.
`therefore cos(tan^(-1)3/4+tan^(-1)2/3)=cos[tan^(-1){(3/4+2/3)/(1-3/4 xx 2/3)}]`
`cos(tan^(-1)17/6)=cos{cos^(-1)6/sqrt(325)=6/(5sqrt(13)) rArr phi =cos^(-1)=6/(5sqrt(13))`
`[therefore tanphi=17/6 rArr cosphi =6/sqrt(325) =6/(5sqrt13))rArr phi=cos^(-1)6/(5sqrt(13)) rArr cosphi=6/(5sqrt(13))]`
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RS AGGARWAL-INVERSE TRIGNOMETRIC FUNCTIONS -Objective Questons
  1. Prove the following results: tan(cos^(-1)""4/5+tan^(-1)""2/3)=(17)/6...

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  2. Find the principal value of: cos^(-1)((sqrt(3))/2)

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  3. Find the principal value of the following: (i) cosec^(-1)(2) (ii) ta...

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  4. Find the principal value of: cos^(-1)(-1/(sqrt(2)))

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  5. Find the principal value of: sin^(-1)(-1/2)

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  6. The principal value of cos^(-1)(-1/2) is

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  7. The principal value of tan^-1(-sqrt3) is

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  8. The principal value of cot^(-1)(-1) is

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  9. Find the principal value of sec^(-1)((-2)/(sqrt(3)))

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  10. The principal value of "cosec"^(-1)(-sqrt(2)) is

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  11. Find the principal values of each of the following: cot^(-1)(-sqrt(...

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  12. The principle value of sin ^(-1)(sin ""(2pi)/(3)) is

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  13. The value of cos^(-1)(cos(14pi/6)) is

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  14. The value of tan^(-1)(tan(8*pi/6)) is

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  15. Find the value of : cot^(-1), (5pi/4)

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  16. The value of sec^(-1)(sec(8pi)/5) is

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  17. The value of "cosec"^(-1)("cosec"(4pi)/3) is

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  18. प्रश्न संख्या 16 से 18में दिए प्रत्येक व्यंजन का मान ज्ञात कीजिए : t...

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  19. pi/3-sin^(-1)(-1/2)=?

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  20. The value of sin(sin^(-1)(1/2)+cos^(-1)(1/2))=?

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  21. If x ne 0 then cos(tan^(-1)+cot^(-1)x)=?

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