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Let fk(x)=(1)/(k)(sin^k x+ cos^k x) " wh...

Let `f_k(x)=(1)/(k)(sin^k x+ cos^k x) " where " x in R and k ge 1 `. Then `f_4(x)-f_6(x)` equals

A

`(1)/(4)`

B

`(1)/(12)`

C

`(1)/6`

D

`(1)/3`

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The correct Answer is:
B
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DIPTI PUBLICATION ( AP EAMET)-TRIGONOMETRIC RATIOS AND IDENTITIES -EXERCISE 1 A ( TRIGONOMETRIC FUNCTIONS)
  1. sqrt((1+sinA)/(1-sin A ))=

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  2. If sqrt((1+ cos theta )/(1- cos theta ))="cosec " theta + cot theta " ...

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  3. If x=a cos^(3) theta , y= a sin^(3) theta then

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  4. If x= a cos^(4) theta, y=bsin^(4) theta , then sqrt(x//a) + sqrt(y//...

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  5. If x cos theta + y sin theta = a , x sin theta - y cos theta = b the...

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  6. If sin theta + cos theta = m and sec theta + " cosec " theta = n the...

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  7. If (x)/(a) cos theta + (y)/(b) sin theta = 1 , (x)/(a) sin theta - (y...

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  8. If x=a("cosec" theta + cot theta ) , y=b( " cosec " theta - cot theta ...

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  9. If x sec theta + y tan theta = a, x tan theta + y sec theta = b " the...

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  10. By eleminating theta from the equation a1 "cosec " theta + b1 cot th...

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  11. If x= a ( sec theta + tan theta )^2 , y=b(sec theta - tan theta )^2 "...

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  12. If tan theta + sin theta = m, tan theta - sin theta = n " then " (m^(...

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  13. If x= cot theta + cos theta , y= cot theta - cos theta , " then " (x^...

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  14. If cot theta + tan theta = m , sec theta - cos theta = n " then " (m^...

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  15. If "cosec " theta - sin theta = m, sec theta - cos theta =n , " then ...

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  16. If a=x cos^(2) alpha + ysin^(2) alpha " then " (x-a)(y-a)+(x-y)^(2)si...

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  17. If x= a cos^(2) theta sin theta and y= a sin^(2) theta cos theta , "...

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  18. If x=r cos theta cos phi , y=r cos theta sin phi and z=r sin theta , ...

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  19. If x=r cos alpha cos beta cos gamma , y= cos alpha cos beta sin gamma...

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  20. Let fk(x)=(1)/(k)(sin^k x+ cos^k x) " where " x in R and k ge 1 . Then...

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