- #1

tellmesomething

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- Homework Statement
- Range of ##\displaystyle \left| \dfrac{(√(cosx)-√(sinx))(√(cosx)+√(sinx))} {3(cosx+sinx)} \right|##

- Relevant Equations
- None

I resolved the numerator to ## cosx-sinx##

We get $$mod\frac{cosx-sinx} {3(cosx+sinx)} $$

If we divide the numerator and denominator by cosx we get

$$mod\frac{1-tanx} {3(1+tanx)}$$(eq1)

We know that tan(π/4-x) is same as ##\frac{1-tanx} {1+tanx}##

So re writing eq1 we get

$$mod\frac{tan(π/4-x} {3}$$

As we know tangent function can take any value from -∞ to+∞

Considering the modulus function we can conclude that the range is 0 to ∞

However thats not the case ofcourse. I graphed it on desmos and while the original question lies on the graph of this simplified tan function, its range is bounded

Please tell me where I went wrong?

We get $$mod\frac{cosx-sinx} {3(cosx+sinx)} $$

If we divide the numerator and denominator by cosx we get

$$mod\frac{1-tanx} {3(1+tanx)}$$(eq1)

We know that tan(π/4-x) is same as ##\frac{1-tanx} {1+tanx}##

So re writing eq1 we get

$$mod\frac{tan(π/4-x} {3}$$

As we know tangent function can take any value from -∞ to+∞

Considering the modulus function we can conclude that the range is 0 to ∞

However thats not the case ofcourse. I graphed it on desmos and while the original question lies on the graph of this simplified tan function, its range is bounded

Please tell me where I went wrong?