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If (a^(2)+1)/(2a)=costheta, then (a^(6)+...

If `(a^(2)+1)/(2a)=costheta, then (a^(6)+1)/(2a^(3))=`

A

`cos^(2) theta`

B

`cos^(3)theta`

C

`cos 2 theta`

D

`cos 3theta`

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The correct Answer is:
D
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If sintheta+costheta=a and (sintheta+costheta)/(sinthetacostheta)=b , then (a) b=(2a)/(a^2-1) (b) a=(2b)/(b^2-1) (c) ab=b^2-1 (d) a+b=1

sintheta+costheta=(sqrt(3)+1)/(2)

i) Prove that: (1-sin2A)/(1+sin2A) = tan^(2)(pi/4-A) ii) If costheta=1/2(x+1/x) , then prove that: cos2theta=1/2(x^(2)+1/x^(2)) and cos3theta=1/2(x^(3)+1/x^(3))

Sides a , b , c of !ABC are in A.P. and costheta_(1)=a/(b+c)costheta_(2)=b/(a+c),costheta_(3)=c/(a+b) , then tan^(2)(theta_(1))/2+tan^(2)(theta_(3))/2 =

The value of (a^(2/3) +2a^(1/2)+3a^(1/3) +2a^(1/6)+1)(a^(1/3)-2a^(1/6)+1)-a^(1/2)(a^(1/2)-2) , when a = 7, is: (a^(2/3) +2a^(1/2)+3a^(1/3) +2a^(1/6)+1)(a^(1/3)-2a^(1/6)+1)-a^(1/2)(a^(1/2)-2) , का मान ज्ञात कीजिए, जब a= 7 है:

costheta(tantheta+2)(2tantheta+1)=?

OBJECTIVE RD SHARMA-TRIGONOMETRIC RATIOS AND IDENTITIES-Chapter Test
  1. The vlaue of cos^(2)76^(@)+cos^(2)16-cos76^(@)cos16^(@),is

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  2. The value of sum(k=1)^(3) cos^(2)(2k-1)(pi)/(12), is

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  3. If (a^(2)+1)/(2a)=costheta, then (a^(6)+1)/(2a^(3))=

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  4. The value of (1)/(cos290^(@))+(1)/(sqrt3sin250^(@)) is equal to

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  5. If tan alpha=(1+2^(-x))^(-1), tan beta=(1+2^(x+1))^(-1) then alpha+bet...

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  6. A and B are positive acute angles satisfying the equations 3cos^(2)A...

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  7. If T(n)=cos^(n)theta+sin ^(n)theta, then 2T(6)-3T(4)+1=

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  8. The maximum value of 1+8sin^(2)x^(2)cos^(2)x^(2) is

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  9. Let thetain(0,pi//4)and t(1)=(tantheta)^(tantheta), t(2)=(tantheta)^(...

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  10. The expression 3{sin^(6)""((pi)/(2)+alpha)+sin^(6)(5pi-alpha) is equal...

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  11. The minimum value of (1)/(3sintheta-4costheta+7), is

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  12. The maximum value of cos^(2)A+cos^(2)B-cos^(2)C, is

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  13. If cos(alpha+beta)sin(gamma+delta)=cos(alpha-beta)sin(gamma-delta) the...

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  14. cosx{(cosx)/(1-sinx)+(1-sinx)/(cosx)}, is

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  15. If tanx=b/athen sqrt((a+b)/(a-b"))+sqrt((a-b)/(a+b))=

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  16. In tantheta+sec theta=sqrt3,0ltthetaltpi, then theta is equal to

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  17. If sqrt3sin theta+costhetagt0, then theta lies in the interval

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  18. Let 0lt x lepi//4, (sec 2x-tan2x) equals

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  19. If n is an odd positive interger, then ((cosA+cosB)/(sinA-sinB))^(n)...

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  20. If 3 tan (theta-15^(@))=tan(theta+15^(@)), 0lt thetalt pi,then theta=

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