Math Trigo question desperately need help thanks!!!!!!!!

[Troubled Student]

How to prove that 1/2(1+sin^2 x) + 1/2(1+cos^2 x) + 1/2(1+sec^2 x)+ 1/2(1+cosec^2 x) = 1

 

[srmichael]

How to prove that 1/2(1+sin^2 x) + 1/2(1+cos^2 x) + 1/2(1+sec^2 x)+ 1/2(1+cosec^2 x) = 1

What have you tried so far? We need to know where you are stuck before we can help.

 

[Troubled Student]

What have you tried so far? We need to know where you are stuck before we can help.

I tried to combine them together, but it got very long and confusing

 

[srmichael]

How to prove that 1/2(1+sin^2 x) + 1/2(1+cos^2 x) + 1/2(1+sec^2 x)+ 1/2(1+cosec^2 x) = 1

I probably should have asked this first, but is this equation [A] or ?

[A]: \(\displaystyle \frac{1}{2}(1+sin^2x)+\frac{1}{2}(1+cos^2x)+\frac{1}{2}(1+sec^2x)+\frac{1}{2}(1+csc^2x)=1\)

OR

: \(\displaystyle \frac{1}{2(1+sin^2x)}+\frac{1}{2(1+cos^2x)}+\frac{1}{2(1+sec^2x)}+\frac{1}{2(1+csc^2x)}=1\)

 

[mmm4444bot]

Whoops -- It looks like you somehow missed reading our FORUM GUIDELINES. Please check 'em out, before proceeding to post again. :cool:

 

[mmm4444bot]

I tried to combine them

Please show us the first two or three steps that you tried.

 

[HallsofIvy]

How to prove that 1/2(1+sin^2 x) + 1/2(1+cos^2 x) + 1/2(1+sec^2 x)+ 1/2(1+cosec^2 x) = 1

It must be \(\displaystyle \frac{1}{2(1+ sin^2 x)}+ \frac{1}{2(1+ cos^2 x)}+ \frac{1}{2(1+ sec^2 x)}+ \frac{1}{2(1+ cosec^2 x)}= 1\) because \(\displaystyle \frac{1}{2}(1+ sin^2 x)+ \frac{1}{2}(1+ cos^2 x)+ \frac{1}{2}(1+ sec^2 x)+ \frac{1}{2}(1+ cosec^2 x)= 1\) is not true.

 

[mmm4444bot]

:idea: My first step would be rewriting secant and cosecant according to basic identities.

I'm waiting for the poster to show something.