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If f(x)=(cos^2x+sin^4x)/(sin^2 x+cos^4x)...

If `f(x)=(cos^2x+sin^4x)/(sin^2 x+cos^4x),` for `x in R,` then f(2002) is equal to

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We know that,
`sin^2x+cos^2x=1`
Given that,
`f(x)=(cos^2x+sin^4x)/(sin^2 x+cos^4x)`
...
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Knowledge Check

  • If f(x) = (cos^2 x +sin^(4) x)/(sin^2 x + cos^4 x) for x in R then number of solution of the equation |sin x| = f(x) in [-2pi , 2pi] is

    A
    2
    B
    3
    C
    4
    D
    5

  • If f(x)=(sin^(4)x+cos^(2)x)/(sin^(2)x+cos^(4)x)"for "x in R , then f(2010)

    A
    1
    B
    2
    C
    3
    D
    4
    • RD SHARMA-FUNCTIONS-Solved Examples And Exercises
    1. If f(x)=(cos^2x+sin^4x)/(sin^2 x+cos^4x), for x in R, then f(2002) is ...

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    2. The range of the function f(x)=(x^2-x)/(x^2+2x) is R (b) R-[1] (c) R={...

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    3. If f(x)=cos(logx), then value of f(x) f(4)-1/2{f(x/4)+f(4x)} is (a) 1...

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    4. If f(x)=log((1+x)/(1-x)) and then f((2x)/(1+x^2)) is equal to {f(x)}^...

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    5. If 2f(x)-3f(1/x)=x^2(x!=0), then f(2) is equal to (a)-7/4("b")""5/...

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    6. If f(x)=(2^x+2^(-x))/2 , then f(x+y)f(x-y) is equals to (a) 1/2{f(2...

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    7. Let f(x)=(alphax)/(x+1),x!=-1. Then write the value of alpha satisfyin...

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    8. Write the range of the function f(x)=sin[x],w h e r e(-pi)/4lt=xlt=pi/...

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    9. If f(x)=log((1+x)/(1-x))a n dg(x)=((3x+x^3)/(1+3x^2)) , then f(g(x)) i...

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    10. If f(x) = cos(log x) then f(x^2)f(y^2)-1/2[f(x^2y^2)+f(x^2/y^2)] has t...

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    11. Relation between graphs of a function and its inverse

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    12. A be the set of two positive integers and f: A -> Z^+ (set of positiv...

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    13. Range of f(x) =1/(1-2cosx) is (1) [1/3,1] (2) [-1,1/3] (3) (-o...

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    14. Let f:[2,oo) rarr R and g:[-2,oo) rarr R be to two real functions defi...

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    15. Find the domain of each of the following real valued functions of real...

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    16. Examples :- If x;yin{1;2;3;4};then which of the following are function...

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    17. Find the domain and range of the function f={(x :1/(1-x^2)): x in R ...

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    18. Express the following functions as sets of ordered pairs and determine...

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    19. if for nonzero x, af(x) + bf(1/x) =1/x-5, where a!=b then f(2) =

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    20. If f(x) = (a-x^n)^(1/n), a > 0 and n in N, then prove that f(f(x)) = x...

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