Question

Explain this:
S/(S²+cos²)
= sec²Θ / (S²sec²Θ + 1)
= sec²Θ / [(S²+1)+S²tan²Θ]

Answer 1

\[\frac{S}{(S^2 + cos^2 \theta)}\] = \[\frac{S}{S^2 + \frac{1}{sec^2 \theta}}\]
Because \(cos^2 \theta = \frac{1}{sec^2 \theta}\)

Then
\[\frac{S*sec^2 \theta}{sec^2 \theta *S^2 + 1}\]

= \[\frac{S*sec^2 \theta}{S^2 *(1 + tan^2 \theta) + 1}\]

Because \(1 + tan^2 \theta = sec^2 \theta\)

And then
= \[\frac{S*sec^2 \theta}{(S^2+1) + S^2*tan^2 \theta}\]

Understood? :)

Answer 2

Mother of explanation.....
Thank you !!!

Answer 3

:)