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For any angle theta the expression (2cos...

For any angle `theta` the expression `(2cos8theta+1)/(2costheta+1)` is eqaul to

A

`(2costheta+)(2cos2theta+1)(2cos4theta+1)`

B

`(costheta-1)(cos2theta-1)(cos4theta-1)`

C

`(2costheta-1)(2cos2theta-1)(2cos4theta-1)`

D

`(2costheta+1)(2cos2theta+1)(cos4theta+1)`

Text Solution

Verified by Experts

The correct Answer is:
C
We have , `(2cos8theta+1)/(2costheta+1)=(2(2cos^(2)4theta-1)+1)/((2costheta+1))`
`=((2cos4theta-1)(2cos4theta+1))/((2costheta+1))`
`=((2cos4theta-1)(2cos2theta-1)(2cos2theta+1))/((2costheta+1))`
`=([((2 cos 4 theta-1)(2 cos 2 theta-1)),((2 cos theta-1)(2 cos theta+1))])/((2cos theta+1))`
`=(2cos4theta-1)(2cos2theta-1)(2costheta-1)`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-TRIGONOMETRIC FUNCTIONS OF COMPOUND ANGLES-Exercise 2 (MISCELLANEOUS PROBLEMS)
  1. For any angle theta the expression (2cos8theta+1)/(2costheta+1) is eqa...

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  2. If sinA+sinB=C,cosA+cosB=D, then the value of sin(A+B)=

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  3. If theta lies in the first quardrant and costheta=(8)/( 17 ), then fi...

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  4. If tanx+tan((pi)/(3)-x)+tan((2pi)/(3)+x)=3, then

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  5. If sin(theta+alpha)=a andsin(theta+beta)=b, then prove that cos(alpha...

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  6. The expression cos^(2)(A-B)+cos^(2)B-2cos(A-B)cosAcosB is

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  7. If tanalpha,tanbeta are the roots of the equation x^(2)+px+q=0(pne0), ...

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  8. If cos(A-B)=3/5 and tanA .tan B=2, then

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  9. tan100^0+tan125^0+tan100^0tan125^0 is equal to

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  10. If pi/2 lt alpha lt pi, pi lt beta lt 3pi/2; sin alpha = 15/17 and tan...

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  11. If sintheta=(12)/(13),(0ltthetalt(pi)/(2))and cosphi=-(3)/(5),(piltph...

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  12. If tanA-tan B=x, and cot B-cotA=y, then find the value of cot(A-B).

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  13. sin4theta can be written as

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  14. If cos 2B =cos(A+C)/cos( A-C), then tanA, tanB, tanC are in

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  15. If (2sinalpha)/({1+cosalpha+sinalpha})=y, then ({1-cosalpha+sinalph...

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  16. (sintheta+sin2theta)/(1+costheta+cos2theta)=

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  17. (sin3theta-cos3theta)/(sintheta+costheta)+1=

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  18. If tanalpha=(1)/(7) and tanbeta=(1)/(3), then cos2alpha is equal to

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  19. If tanbeta=costhetatanalpha, then "tan"^(2)(theta)/(2)=

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  20. sec^2 A(1+sec2A) = 2sec2A

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  21. 2sinAcos^3A-2sin^3AcosA=

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