Question

tan^2.cos^2=1-cos^2​

Answer 1

Answer:

$\fcolorbox {red} {green} {Answer}$

$\boxed{To\:Proove\::\:tan^2cos^2 = 1-cos^2}$

$\red{\text {=> \frac{sin^2}{cos^2}\: cos^2}}$

$\blue{=> sin^2}$

$\orange {=> 1-cos^2}$

$\boxed{Hence\:Prooved}$

Answer 2

Answer:

$tan {}^{2} x \times cos {}^{2} x = 1 - cos {}^{2} x \\ take \: lhs = tan {}^{2} x \times cos {}^{2} x \\ = \frac{sin {}^{2} x}{cos {}^{2}x } \times cos {}^{2} x \\ = sin {}^{2} \\ we \: know \: that \: sin {}^{2} x + cos {}^{2} x = 1 \\ hence \: sin {}^{2} x = 1 - cos {}^{2} x = rhs \\ hence \: proved$

Thanks!