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If f(x)=2(7cosx+24sinx)(7sinx-24cosx), f...

If `f(x)=2(7cosx+24sinx)(7sinx-24cosx),` for every `x in R ,` then maximum value of `f(x)^(1/4)` is_____

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The correct Answer is:
625
`f(x) = 2(7 cos x + 24 sin x ) (7 sinx - 24 cos x )`
Let `r cos theta = 7 , r sin theta = 24`
`therefore r ^(2) = 625 , tan theta = (24)/(7)`
`therefore f(x) = 2rcos (x- theta) xx r sin (x- theta)`
`= r^(2) ( sin 2 (x - theta))`
`f(x)_(max)= 25^(2)`
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CENGAGE-TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS-Exercise (Numerical)
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  2. If f(x)=2(7cosx+24sinx)(7sinx-24cosx), for every x in R , then maximu...

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  3. In a triangle A B C ,/C=pi/2dot If tan(A/2)a n dtan(B/2) are the roots...

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  4. If x , y in R satisfies (x+5)^2+(y-12)^2=(14)^2, then the minimum val...

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  5. Suppose x and y real number such that tan x tan y=42 and cot x +cot =4...

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  6. Let 0lt=a , b , c ,dlt=pi, where ba n dc are not complementary, such t...

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  7. Suppose A and B are two angles such that A , B in (0,pi) and satisfy s...

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  8. alphaa n dbeta are the positive acute angles and satisfying equation 5...

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  9. The absolute value of the expression tanpi/(16)+tan(5pi)/(16)+tan(9pi)...

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  10. The greatest integer less than or equal to 1/(cos290^0)+1/(sqrt(3)sin2...

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  11. The maximum value of y=1/(sin^6x+cos^6x) is

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  12. The maximum value of cos^2(45^0+x)+(sinx-cosx)^2 is

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  13. Find the exact value of coses 10^(@)+"coses"50^(@)-"cosec"70^(@)

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  14. Number of triangles A B C if tanA=x ,tanB=x+1,a n dtanC=1-x is

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  15. If log(10) sin x+log(10)cos x=-1 and log(10)(sinx+cosx)=(log(10)n-1)/2...

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  16. The value of (sin 1^(@) +sin 3^(@) + sin 5^(@) +sin 7^(@))/(cos 1^(@)*...

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  17. In a triangle A B C , if A-B=120^0a n dsinA/2sinB/2sinC/2=1/(32), then...

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  18. If (tanx)/2=(tany)/3=(tanz)/5,x+y+z=pia n dtan^2x+tan^2y+tan^2z=(38)/K...

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  19. If sin^3xcos3x+cos^3xsin3x=3/8, then the value of 8sin4x is

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  20. The value of cos e cpi/(18)-4sin(7pi)/(18) is

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