Question

Prove:
sec^4 theta - tan^4 theta = 2sec^2 theta -1

Answer 1

\[LHS = \sec^4\theta-\tan^4\theta\]\[=\left( \sec^2\theta+\tan^2\theta \right)\left( \sec^2\theta-\tan^2\theta \right)\]

Answer 2

can you take it from there......

Answer 3

\[\sin^2\theta+\cos^2\theta = 1\]
divide everything with \(\cos^2\theta\) gives you\[\implies \tan^2\theta +1=\sec^2\theta\ \dots\Huge\star\]
using this equation you can see that \(\left( \sec^2\theta-\tan^2\theta \right)=1\)

and \(\tan^2\theta\) can be replaced with \(\large\sec^2\theta-1\)

Answer 4

so is it sec^2 -1

Answer 5

(sec2theta-tan2theta)*(sec2theta+tan2theta)
1*(sec2theta+sec2theta-1)
2sec2theta-1