Question

Prove that --
sec^2ø-tan^2ø=1

Answer 1

Explanation:

We know that sin²Ф+cos²Ф=1

when you divide both sides by cos²Ф you get

sin²Ф/cos²Ф+cos²Ф/cos²Ф=1/cos²²Ф

sin²Ф/cos²Ф=tan²Ф

cos²Ф/cos²Ф=1

1/cos²Ф=sec²Ф

tan²Ф+1=sec²Ф

subtract tan²Ф on both sides

1=sec²Ф-tan²Ф

therefore sec²Ф-tan²Ф=1