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If f(x)=cos^2x+s e c^2x ,t h e n (a)f(x...

If `f(x)=cos^2x+s e c^2x ,t h e n` `(a)f(x)<1` (b) `f(x)=1` (c) `2ltf(x)<1` (d) `""""f(x)ge2`

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To solve the problem, we need to analyze the function \( f(x) = \cos^2 x + \sec^2 x \). ### Step 1: Rewrite the function We know that \( \sec^2 x = \frac{1}{\cos^2 x} \). Therefore, we can rewrite the function as: \[ f(x) = \cos^2 x + \frac{1}{\cos^2 x} \] ...
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RD SHARMA-TRIGONOMETRIC FUNCTIONS-Solved Examples And Exercises
  1. If A lies in second quadrant and 3tanA+4=0, then the value of 2cotA-5c...

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  2. Which of the following is correct? s in1^0> s in1 (b) s in1^0<s in1 ...

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  3. If f(x)=cos^2x+s e c^2x ,t h e n (a)f(x)<1 (b) f(x)=1 (c) 2ltf(x)<1...

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  4. If sectheta=x+1/(4x), then s e ctheta+t a ntheta= (a)x ,1/x (b) 2x ,...

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  5. If s e c^2theta=(4x y)/((x+y)^2) is true if and only if x+y!=0 (b) x=...

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  6. If cos e cx+cotx=(11)/2 , then t a nx= (a)(21)/(22) (b) (15)/(16) (...

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  7. If (3pi)/4ltalphaltpi, t h e nsqrt(2cotalpha+1/(sin^2alpha)) is equal ...

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  8. If x=rsinthetacosphi,y=rsinthetasinphi and z=rcostheta, then x^2+y^2+...

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  9. If sintheta+costheta=0 and theta lies in the fourth quadrant, find si...

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  10. Prove that: sqrt((1-sintheta)/(1+sintheta))+sqrt((1+sintheta)/(1-sinth...

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  11. Prove that: cos((3pi)/2+x)cos(2pi+x){cot((3pi)/2-x)+"cot"(2pi+x)}=1

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  12. Prove that: (cos(pi+x)cos(-x))/(sin(pi-x)cos(pi/2+x) = cot^2x

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  13. If x=(2sintheta)/(1+costheta+sintheta) , then prove that (1-costheta+...

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  14. If tanx=(b)/(a), then find the value of sqrt((a+b)/( a-b ))+sqrt((a-b)...

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  15. Find the values of the following trigonometric ratios. (i)cosec390^0 ...

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  16. Prove that: sin(-420^0)(cos390^0)+cos(-660^0)(sin330^0)=-1.

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  17. Prove that: "sec"((3pi)/2-theta)"sec"(theta-(5pi)/2)+t a n((5pi)/2+the...

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  18. Find the value of : sin^2(pi/(18))+sin^2(pi/9)+sin^2((7pi)/(18))+sin^2...

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  19. If any quadrilateral ABCD, prove that "sin"(A+B)+sin(C+D)=0 "cos"(A...

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  20. Find the value of the expression 3{sin^4((3pi)/2-theta)+sin^4(3pi+the...

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