Question

Ok.. So I see a recurring theme that we do not cover in any of my lecture notes. This is a trig function. COS²θ - SIN²θ = 1 I have to demonstrate why COS²θ MINUS SIN²θ = 1... But every transformation I make leads me to believe that this can never be true. Help?

Answer 1

Because the actual identity says
`\sin ^(2)\theta +\cos ^(2)\theta = 1`

Explanation:

The trigonometric ratios
`\sin \theta` and
`\cos\theta` have a maximum value of 1. And hence
`\cos^(2)\theta` and
`\sin^(2)\theta` will have values between 0 and 1 as they are squares and will be always positive.

But if we look at the equation
`\cos^(2)\theta-\sin^(2)\theta=1` shows that
`\cos^(2)\theta` will be more than 1. Hence it is an incorrect equation.

The correct relation between
`\cos^(2)\theta` and
`\sin^(2)\theta` is
`\sin ^(2)\theta +\cos ^(2)\theta = 1`.