Prove the following: tan⁴theta+tan²theta=sec⁴theta-sec²theta
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Given,
tan⁴∅+tan²∅=sec⁴∅-sec²∅
L.H.S
sec⁴∅-sec²∅
→
→
sec²∅(sec²∅-1)
→
(1+tan²∅)(1+tan²-1) [∴sec²∅-1+tan²∅]
(1+tan²∅)(tan²∅)
→
tan²∅+tan⁴∅
→
L.H.S=R.H.S
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