Question

Good people please help me!!!! ​

Answer 1

a) |sec(θ)|

b) 2cot(2x)

Explanation:

Trig identities are used to simplify these expressions. Several are used:

• tan(180°-x) = -tan(x)
• cot(90°-x) = tan(x)
• 1 +tan(x)² = sec(x)²
• tan(x) = sin(x)/cos(x)
• sin(2x) = 2sin(x)cos(x)
• cot(x) = cos(x)/sin(x)

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a.

`√(1-\tan(180^\circ-\theta)\cot(90^\circ-\theta))=√(1-(-\tan(\theta))\tan(\theta))\\\\=√(1+\tan^2(\theta))=√(\sec^2(\theta))=\boxed`

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b.

`(\cos(2x)\tan(x))/(\sin^2(x))=(\cos(2x))/(\sin^2(x))\cdot(\sin(x))/(\cos(x))=(\cos(2x))/(\sin(x)\cos(x))\\\\=(\cos(2x))/(\left((\sin(2x))/(2)\right))=2(\cos(2x))/(\sin(2x))=\boxed{2\cot(2x)}`