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For acute angle theta, Prove that sinthe...

For acute angle `theta`, Prove that `sinthetaltthetalttantheta`.

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Consider the circle with unit radius as show in the following figure.
From the figure, from position of C on the circle
Area of `DeltaOBClt" Area of sector " Delta OBD`
`:. 1/2(CE)(OB)lt1/2thetalt1/2(OB)(BD)`
`rArr1/2(sintheta)(1)lt1/2thetalt1/2(1)(tantheta)`
`rArr sinthetaltthetalttantheta`
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CENGAGE-TRIGONOMETRIC FUNCTIONS -SINGLE CORRECT ANSWER TYPE
  1. For acute angle theta, Prove that sinthetaltthetalttantheta.

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  2. The circular wire of diameter 10 cm is cut and placed along the circum...

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  3. sintheta/(1-cottheta)+costheta/(1-tantheta)= (a)theta (b)1 (c)costh...

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  4. If theta in (pi//4, pi//2) and sum(n=1)^(oo)(1)/(tan^(n)theta)=sin the...

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  5. The value of (tan^(2)20^(@)-sin^(2)20^(@))/(tan^(2)20^(@).sin^(2)20^(@...

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  6. If 15 sin^(4)alpha+10cos^(4)alpha=6, then the value of 8 cosec^(6)alph...

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  7. In DeltaABC, if sin A + sin B + sin C= 1 + sqrt2 and cos A+cos B+cos...

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  8. If (sin^(2)x-2cos^(2)x+1)/(sin^(2)x+2cos^(2)x-1)=4, then the value of ...

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  9. If sintheta,tantheta,costheta are in G.P. then 4sin^2theta-3sin^4theta...

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  10. If tantheta-cottheta=aandsintheta+costheta=b(b^2-1)^2(a^2+4) is equal...

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  11. The least value of 18 sin^(2)theta+2 cosec^(2)theta-3 is

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  12. If tan^2 alpha tan^2 beta + tan^2 beta tan^2 gamma + tan^2 gamma tan^2...

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  13. If x,y,z be all positive acute angles then the least value of tanx(cot...

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  14. Three circles each of radius 1, touch one another externally and they ...

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  15. If (cos alpha)/(cos A)+(sin alpha)/(sin A)+(sin beta)/(sin A)=1, where...

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  16. Consider angles alpha = (2n+(1)/(2))pi pm A and beta = m pi +(-1)^(m)(...

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  17. Which of the following is true ?

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  18. If the angle A of a triangle ABC is given by the equation 5 cos A + 3 ...

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  19. Which of the following is greatest ?

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  20. The number of value/values of x for which sin y=x^(2)-2x si possible i...

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  21. Which of the following is not correct ?

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