room $\cos^2 \theta$ and $\cos \theta^2$ the same?I mean be the $\sin,\cos, \tan ,\cot ,\sec,\csc$. Are they same? Please aid a brickandmortarphilly.coms noob here.

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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:

Cos$^2$ refers to $(\cos x)^2$ when Cos describes $\cos (x^2)$.

Should be an extremely careful.


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Trigonometric identity: $\frac \tan\theta1-\cot\theta+\frac \cot\theta1-\tan\theta =1+\sec\theta\cdot\csc\theta$