We need to simplify \(\frac{1-tan^{2}x}{1+tan^{2}x}\)
Solution
\(\frac{1-tan^{2}x}{1+tan^{2}x}\)We know from trigonometric identity that
\(1 + \tan ^{2}x= \sec^{2}x\)Hence the given equation becomes
\(\frac{1-tan^{2}x}{sec^{2}x}\) \(\frac{1}{sec^{2}x} – \frac{tan^{2}x}{sec^{2}x}\)We know that 1 / sec x = cos x and tan x can be expressed as sin x / cos x
=\(\frac{cos^{2}}{x} – \frac{sin^{2}x}{cos^{2}x}\) . cos2x
= cos2x – sin2x
Answer
\(\frac{1-tan^{2}x}{1+tan^{2}x}\) = cos2x – sin2x
