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Let F(x) = f(x) +g(x) , G(x) = f(x) -...

Let `F(x) = f(x) +g(x) , G(x) = f(x) - g( x) and H(x) =(f( x))/( g(x)) `
where `f(x) = 1- 2 sin ^(2) x and g(x) =cos (2x) AA f: R to [-1,1] and g, R to [-1,1] `
Now answer the following
If the solution of F(x) -G (x) =0 are `x_1,x_2, x_3 `--------- `x_n ` Where ` x in [0,5 `pi]` then

A

1)`x_(1), x_(2), x_(3) - - - - - x_(n)` are in A.P with common difference `pi/4`

B

2)the no. of solutions of `F(x)-G(x)=0` is `10 AA x in [0, 5pi]`

C

3)the sum of all solutions of `F(x)-G(x) = 0` is `AA x in [0, 5pi]` is `25 pi`

D

4)b, c are true

Text Solution

Verified by Experts

The correct Answer is:
D
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