Does 2+2tanx=2secx?

2 Answers
MathFact-orials.blogspot.com
May 4, 2017

2+2tanx!=2secx

Explanation:

2+2tanx=2secx ?

2+(2sinx)/cosx=2/(cosx)

(2(cosx))/cosx+(2sinx)/cosx=2/(cosx)

(2cosx+2sinx)/cosx=2/(cosx)

(2(cosx+sinx))/cosx=2/(cosx)

For this to be an identity, cosx+sinx must equal 1 for all values of x. But, for instance, with x=pi/2 => sinx=cosx=sqrt2/2.

sqrt2/2+sqrt2/2=sqrt2!=1

And so the identity is not valid.

2+2tanx!=2secx

Shwetank Mauria
May 4, 2017

Only when x=2nxx360^@, where n is an integer.

Explanation:

No, if you mean 2+2tanx=2secx as an identity it is not.

But we can solve this for x and at some values we may have

2+2tanx=2secx.

As 2+2tanx=2secx

1+tanx=secx

and multiplying by cosx we get

cosx+sinx=1

or sqrt2(cosx xx1/sqrt2+sinx xx1/sqrt2)=1

or cosx xx1/sqrt2+sinx xx1/sqrt2=1/sqrt2

or cosxcos45^@+sinxsin45^@=cos45^@

or cos(x-45^@)=cos45^@

i.e. x-45^@=2nxx360^@+-45^@, where n is an integer.

i.e. x=2nxx360^@=90^@ or x=2nxx360^@

But at first solution, both tanx and secx are not defined

Hence x=2nxx360^@

graph{(y-secx+tanx+1)=0 [-10, 10, -5, 5]}

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