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if cosecθ−cotθ= 1/2 , 0<θ< π/2 then ...

if ` cosecθ−cotθ= 1/2 `, `0<θ< π/2 ` then `cosθ` is equal to

A

`sin(7cos^(-1)f(5))=0`

B

`f(4)=sqrt(3)/2`

C

`underset(ntoinfty)"lim"f(n)=1/2`

D

If `alpha=tan(cos^(-1)f(6))`, then `alpha^(2)+2alpha-1=0`

Text Solution

AI Generated Solution

To solve the equation \( \csc \theta - \cot \theta = \frac{1}{2} \) for \( \cos \theta \) where \( 0 < \theta < \frac{\pi}{2} \), we can follow these steps: ### Step 1: Rewrite the equation in terms of sine and cosine The cosecant and cotangent can be expressed in terms of sine and cosine: \[ \csc \theta = \frac{1}{\sin \theta}, \quad \cot \theta = \frac{\cos \theta}{\sin \theta} \] Substituting these into the equation gives: ...
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