Question

Question 15
Show that: $ta{n}^4\theta +ta{n}^2\theta =se{c}^4\theta -se{c}^2\theta$

Answer 1

$LHS=ta{n}^4\theta +ta{n}^2\theta =ta{n}^2\theta (ta{n}^2\theta +1)$

$=ta{n}^2\theta .se{c}^2\theta$ $[\because se{c}^2\theta =ta{n}^2\theta +1]$

$=(se{c}^2\theta -1)se{c}^2\theta$ $[\because ta{n}^2\theta =se{c}^2\theta -1]$

$=se{c}^4\theta -se{c}^2\theta =RHS$