Trigonometry - Identities

EXAMPLE

Show that

Start with the complicated side

Need to recognise that    cos⁴t - sin⁴t
can be written as the difference of two squares    (cos²t - sin²t)(cos²t + sin²t)

Need to recognise that    cos²t + sin²t = 1

Which is the same as

Looking back at the question to see what is required we see that it is    cot² + 1
Thus we need two terms in the answer
and we can create these two terms by writing separate fractions

cos²t / sin²t = cot²t    and    sin²t / sin²t = 1

This example is shown as the third example on the video below