Answer:
steps below
Step-by-step explanation:
7. sin⁴α+2sin²α cos²α + cos⁴α
==> = (sin²α + cos²α)²
==> = 1
12. sec⁶A - tan⁶A = (sec²a-tan²A)(sec⁴A+sec²A tan²A+tan⁴A)
==> = ((1-sin²A)/cos²A) ( (sec⁴A-2sec²A tan²A+tan⁴A) + 3(sec²A tan²A))
==> = (cos²A/cos²A) ((sec²a-tan²A) + 3(sec²A tan²A))
==> = 1* (1 + 3(sec²A tan²A))
==> = 1 + 3(sec²A tan²A)
14. (1-tanθ) / (1+tanθ) = ((cotθ - 1)/cotθ) / ((cotθ + 1)/cotθ)
==> = (cotθ - 1) / (cotθ + 1)
