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Prove that (4cos^2 9^0-3)(4cos^2 27^0-3)...

Prove that `(4cos^2 9^0-3)(4cos^2 27^0-3)=tan9^0dot`

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Prove that (4cos^(2)9^(@)-3)(4cos^(2)27^(0)-3)=tan9^(@)

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Prove that (4 cos^(2)9^(@)-3)(4 cos ^(2)27^(@)-3)=tan 9^(@) .

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Prove that tan9^(0)-tan27^(0)-cot27^(0)+cot9^(0)=4

Prove that :cos9^(0)+sin9^(0)=sqrt(2)sin54^(@)

Find the value of (4cos^(2)9^(@)-1)(4cos^(2)27^(@)-1) (4cos^(2)81^(@)-1)(4cos^(2)243^(@)-1) .

If sin alpha =(1)/(2) , prove that (3 cos alpha - 4 cos ^(3) alpha )=0.

Find the value of log_(sqrt(3))((4cos^(2)9^(@)-1)(4cos^(2)27^(@)-1)(4cos^(2)81^(@)-1)(4cos^(2)243^(@)-1))

ALLEN-BASIC MATHS,LOGARITHIM, TRIGNOMETRIC RATIO AND IDENTITIES AND TRIGNOMETRIC EQUATION -EXERCISE (S-1)
  1. If cos(alpha+beta)=4/5; sin(alpha-beta)=5/13 and alpha,beta lie betwee...

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  2. If the value of the expression sin 25^@* sin 35^@* sin 85^@ can be exp...

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  3. Prove that (4cos^2 9^0-3)(4cos^2 27^0-3)=tan9^0dot

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  4. Prove that 4cos((2pi)/7).cos(pi/7)-1=2cos((2pi)/7).

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  5. Let P(k)=(1+cospi/(4k)) (1+cos((2k-1)pi)/(4k)) (1+cos((2k+1)pi)/(4k))...

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  6. Calculate without using trigonometric tables: (a) 4 cos 20^@ - sqrt3 c...

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  7. (2cos4 0^(@)-cos2 0^(@))/(sin2 0^(@)

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  8. cos^6(pi/16)+cos^6(3pi/16)+cos^6(5pi/16)+cos^6(7pi/16)

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  9. tan1 0^(@)-tan5 0^(@)+tan7 0^(@)

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  10. Given that (1+tan1^@)(1+tan2^@)+...........+(1+tan45^@)= 2^n find n .

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  11. If a leq 3 cos (theta+pi/3)+5cos theta+3 leq b, find a and b, where ...

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  12. Let k=1^@ then prove that sum(n=0)^(88)1/(cosnkcos(n+1)k)=cosk/sin^2k

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  13. If x and y are real number such that x^2 +2xy-y^2=6, find the minimum...

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  14. If A+B+C=pi, prove that tan^2A/2+tan^2B/2+tan^2C/2geq1.

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  15. solve the equation for x , 5^(1/2)+5^(1/2 + log5 sinx) = 15^(1/2 + log...

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  16. Find values of theta satisfying sintheta+sin5theta=sin3theta such that...

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  17. Solve the equality 2sin11 x+cos3x+sqrt(3)sin3x=0.

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  18. Find all value of theta, between 0 & pi, which satisfy the equation;...

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  19. Find the general solution of the equation, 2+tanx.cotx/2.tanx/2=0

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  20. Determine the smallest positive value of x which satisfy the equation ...

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