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Imran writes: "sin² A + cos² A = 1, so taking square roots, sin A + cos A = 1." Find sin 45° + cos…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Imran writes: " $\sin^2 A + \cos^2 A = 1$ , so taking square roots, $\sin A + \cos A = 1$ ." Find $\sin 45^\circ + \cos 45^\circ$ to three decimal places, and explain his mistake.

Need a reminder? The key ideaShow

To prove an identity, start with one side and change it step by step into the other. Write ratios in $\sin A$ and $\cos A$ , use $\sin^2 A + \cos^2 A = 1$ , $1 + \tan^2 A = \sec^2 A$ and $1 + \cot^2 A = \text{cosec}^2 A$ , and factorise. One angle where a claim fails shows it is not an identity.

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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