Does #2+2tanx=2secx#?

2 Answers

#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#

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]}