Question

What is the simplified value of tan (θ/2) + cot (θ/2)?

Answer 1

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Answer 2

Answer: $2 cosec \theta$

Step-by-step explanation:

Here the given expression,

$tan (\frac{\theta}{2}) + cot (\frac{\theta}{2})$

= $\frac{sin (\frac{\theta}{2})}{cos (\frac{\theta}{2})} +\frac{cos (\frac{\theta}{2})}{sin (\frac{\theta}{2})}$

= $\frac{sin^2 (\frac{\theta}{2})+cos^2 (\frac{\theta}{2})}{cos (\frac{\theta}{2}) sin (\frac{\theta}{2})}$

= $\frac{1}{cos (\frac{\theta}{2}) sin (\frac{\theta}{2})}$

= $\frac{2}{2 cos (\frac{\theta}{2}) sin (\frac{\theta}{2})}$

= $\frac{2}{sin\theta}$      ( Because sin 2x = 2 sinx cosx )

= $2 cosec\theta$