verify the identity. \n\\( \\cos x+\\cos x \\tan ^{2} x=\\sec x \\)\nto verify the identity, start with the…

verify the identity. \n\\( \\cos x+\\cos x \\tan ^{2} x=\\sec x \\)\nto verify the identity, start with the more complicated side and transform it to look like the other side. choose the com\n\\( \\cos x+\\cos x \\tan ^{2} x \\)\n\\( =\\cos x(\\square) \\)\n(do not simplify.)\n\\( =\\cos x(\\square) \\)\n\\( =\\square \\)\n(do not simplify.)\n\\( =\\sec x \\)

verify the identity. \n\\( \\cos x+\\cos x \\tan ^{2} x=\\sec x \\)\nto verify the identity, start with the more complicated side and transform it to look like the other side. choose the com\n\\( \\cos x+\\cos x \\tan ^{2} x \\)\n\\( =\\cos x(\\square) \\)\n(do not simplify.)\n\\( =\\cos x(\\square) \\)\n\\( =\\square \\)\n(do not simplify.)\n\\( =\\sec x \\)

Answer

Explanation:

Step1: Factor out (\cos x)

[ \cos x+\cos x\tan^{2}x=\cos x(1 + \tan^{2}x) ]

Step2: Use the Pythagorean identity (1+\tan^{2}x=\sec^{2}x)

[ \cos x(1 + \tan^{2}x)=\cos x\sec^{2}x ]

Step3: Express (\sec x) as (\frac{1}{\cos x})

[ \cos x\sec^{2}x=\cos x\times\frac{1}{\cos^{2}x} ]

Step4: Simplify the expression

[ \cos x\times\frac{1}{\cos^{2}x}=\frac{1}{\cos x}=\sec x ]

Answer:

The identity (\cos x+\cos x\tan^{2}x = \sec x) is verified.