Question

tan theta divided by sec theta minus 1 plus tan theta divided by sec theta plus 1​

Answer 1

Answer:

$\frac{tan\beta }{sec\beta -1}+\frac{tan\beta }{sec\beta +1} = 2cosec\beta$

Step-by-step explanation:

I think your question is $\frac{tan\beta }{sec\beta -1}+\frac{tan\beta }{sec\beta +1}$.

⇒ $\frac{tan\beta(sec\beta+1)+tan\beta(sec\beta-1)}{(sec\beta-1)(sec\beta+1)}$

⇒ $\frac{tan\beta.sec\beta+tan\beta+tan\beta.sec\beta-tan\beta }{(sec\beta)^{2}-1}$

⇒ $\frac{2tan\beta.sec\beta}{tan^{2}\beta}$

⇒ $\frac{2sec\beta}{tan\beta}$

⇒ $2\frac{\frac{1}{cos\beta}}{\frac{sin\beta}{cos\beta}}$

⇒ $\frac{2}{sin\beta}$

⇒ $2cosec\beta$