Show that tan 4 θ +tan 2 θ =sec 4 θ -sec 2 θ .

Question

Philoid · Accepted Answer

L.H.S: tan⁴θ + tan² θ

Taking tan² θ common, we get

tan² θ (tan² θ + 1)

= tan² θ sec² θ [∵ sec² θ – tan² θ = 1 ⇒ tan² θ + 1 = sec² θ]

= (sec² θ – 1) sec² θ [∵tan² θ = sec² θ – 1]

= sec⁴ θ – sec² θ

: R.H.S

Show that tan4 θ +tan2 θ =sec4 θ -sec2 θ.