You are watching: (cos θ + cos θ)2 + (cos θ + cos θ)2
No, they space not the same.
When you form $\cos^2 \theta$ you actually mean $(\cos \theta)^2$.
When you type $\cos \theta^2$ you median $\cos(\theta ^2)$.
The an initial notation is supplied to mean$$\cos^2 \theta = \left( \cos \theta \right)^2$$Your second notation will normally be check out as$$\cos \theta^2 = \cos \left( \theta^2 \right)$$although it is sometimes desired to use the notation in the right-hand side to it is in clear.
They room not the exact same since$$\left( \cos \theta \right)^2 = \cos\theta\cos\theta \ne \cos(\theta\theta) = \cos(\theta^2)$$
It"s a matter of syntax.
In handwriting or literature: $\sin^2 x \equiv (\sin x)^2$ and $\cos x^2 \equiv \cos (x^2)$;
however for computer system software, say brickandmortarphilly.comematica:
Should be an extremely careful.
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Trigonometric identity: $\frac \tan\theta1-\cot\theta+\frac \cot\theta1-\tan\theta =1+\sec\theta\cdot\csc\theta$