Question

For a prism, show that i + e = A + δ.

Answer 1

Answer:

m = (cos∅ - sin∅)

n = (cos∅ + sin∅)

\begin{lgathered}LHS = \sqrt{\frac{m}{n}}+\sqrt{\frac{n}{m}} \\ \\ = \frac{ \sqrt{m} }{ \sqrt{n} } + \frac{ \sqrt{n} }{ \sqrt{m} } \\ \\ = \frac{m + n}{ \sqrt{mn} } \\\end{lgathered}

LHS=

n

m

+

m

n

=

n

m

+

m

n

=

mn

m+n

now, put m =( cos∅ - sin∅) and n = (cos∅ + sin∅)

= {(cos∅ - sin∅)+(cos∅ + sin∅)}/√{cos∅-sin∅)(cos∅+sin∅)}

= 2cos∅/√{cos²∅ - sin²∅}

= 2/√{cos²∅/cos²∅ - sin²∅/cos²∅}

= 2/√{1 - tan²∅} = RHS