tan^4 x + tan^2 x+ 1 = 1 - (Sin^2 x)(Cos^2 x)
Please someone help me solve this one so I can get some sleep tonight! I've been trying for 3 days off and on. Pretty please!
Carol
tan^4Ө + tan^2Ө + 1 = 1 + (sin^2Ө)(cos^2Ө)
Here it is, pasted directly from the homework. If it's false, I will be relieved. Is there a way to prove that it's false?
Carol
Working on the left hand side...
$\displaystyle tan^2x + tan^4x +1$
$\displaystyle = \frac{1}{cos^2x} + tan^4x $ ... the entire left hand side can be manipulated using this.. $\displaystyle 1 +tan^2x= sec^2 x$
$\displaystyle = \frac{1}{cos^2x} + \left(\frac{1}{cos^2x} -1 \right) \left(\frac{1}{cos^2x} -1 \right) $
$\displaystyle = \frac{1}{cos^2x} + \left(\frac{1}{cos^2x} -1 \right) \left(\frac{1}{cos^2x} -1 \right) $
$\displaystyle = \frac{1}{cos^4x} - \frac{1}{cos^2x} +1 $
$\displaystyle = \frac{1}{cos^4x} - tan^2x $
$\displaystyle = 1 $
Is the RHS = 1?