Prove tan²x + 1 = sec²x and cot²x + 1 = cosec²x | A-Level Trig Identities

▶️ Choose Function Derivation:    • The Choose Function explained.   Here are two trig identities you never need to memorise again: tan squared x plus 1 equals sec squared x, and cot squared x plus 1 equals cosec squared x. Both of them drop straight out of one identity you almost certainly know already – sin squared x plus cos squared x equals 1. I'll give you a few seconds to pause and have a go yourself first, then we'll go through it together. Divide by sin squared x and you get the cot and cosec identity; divide by cos squared x instead and you get the tan and sec one. One line of working each. 📝 A quick note: dividing by sin squared x only works when sin x isn't zero, and dividing by cos squared x needs cos x to be non-zero – that's why the identities only hold where tan, sec, cot and cosec are actually defined. If you have any questions, leave them in the comments and I'll get back to you. 📚 Want one-to-one A-level maths tuition? Email me at calcaistermathstutoring@gmail.com Chapters 0:00 Two identities you never need to memorise 0:09 The starting point: sin² x + cos² x = 1 0:11 Pause and try it yourself 0:20 Divide by sin² x: cot² x + 1 = cosec² x 0:37 Divide by cos² x: tan² x + 1 = sec² x 0:53 Recap 1:01 What to watch next #alevelmaths #trigonometry #trigidentities #proof #maths