1. This seems very weird, it's pretty muchthebasic proof.

Therefore if we square both:

Adding them:

By the definition of a right angled triangle and using Pythagoras the right side cancels to 1.

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2. Expand to give:

Remember what is equal to

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3. Rewrite in terms of sin and cos:

Give them the same denominator by cross multiplying

and cancel to give the rhs