Question

If sin^2 theta + cos theta = 1 then what is tan theta?

Answer 1

Answer:

Step-by-step explanation:

We have,

$\tt{sin^2(\theta)+cos(\theta)=1}$

$\tt{\implies\,1-cos^2(\theta)+cos(\theta)=1}$

$\tt{\implies\,-cos^2(\theta)+cos(\theta)=0}$

$\tt{\implies\,cos^2(\theta)-cos(\theta)=0}$

$\tt{\implies\,cos(\theta)\big\{cos(\theta)-1\big\}=0}$

$\tt{\implies\,cos(\theta)=0\,\,\,\,or\,\,\,\,cos(\theta)-1=0}$

$\tt{\implies\,cos(\theta)=0\,\,\,\,or\,\,\,\,cos(\theta)=1}$

$\tt{\implies\,\theta=(2n+1)\dfrac{\pi}{2}\,\,\,\,or\,\,\,\,\theta=2m\pi\,\,\,\,\,\,\,\forall\,m,n\in\mathbb{Z}}$

So,

$\tt{\implies\,tan(\theta)=\infty\,\,\,\,or\,\,\,\,tan(\theta)=0}$