simplify.\ncot²(π/2 − x) + cos²(π/2 − x) + cos²x\n?²x

Explanation:

Step1: Use co - function identities

Recall the co - function identities: (\cot\left(\frac{\pi}{2}-x\right)=\tan x) and (\cos\left(\frac{\pi}{2}-x\right)=\sin x). Substitute these identities into the given expression: The expression (\cot^{2}\left(\frac{\pi}{2}-x\right)+\cos^{2}\left(\frac{\pi}{2}-x\right)+\cos^{2}x) becomes (\tan^{2}x+\sin^{2}x+\cos^{2}x).

Step2: Use the Pythagorean identity (\sin^{2}\theta+\cos^{2}\theta = 1)

We know that (\sin^{2}x+\cos^{2}x = 1). So the expression (\tan^{2}x+\sin^{2}x+\cos^{2}x) can be rewritten as (\tan^{2}x + 1).

Step3: Use the Pythagorean identity (1+\tan^{2}\theta=\sec^{2}\theta)

Since (1+\tan^{2}x=\sec^{2}x), the simplified form of the original expression is (\sec^{2}x).

Answer:

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