1.

If x Sin (90° – θ) Cot (90° – θ) = Cos (90° – θ) then x = A) 0 B) 1 C) – 1 D) 2

Answer»

Correct option is: B) 1

Given that 

x sin (\(90^\circ\) - \(\theta\)) cot(\(90^\circ\) - \(\theta\)) = cos (\(90^\circ\) - \(\theta\))

= x cos \(\theta\) tan \(\theta\) = sin \(\theta\)

(\(\because\) cos (\(90^\circ\) - \(\theta\)) = sin \(\theta\), sin (\(90^\circ\) - \(\theta\)) = cos \(\theta\), cot (\(90^\circ\) - \(\theta\)) = tan \(\theta\))

= x cos \(\theta\) \(\frac {sin \, \theta}{cos \, \theta} = sin \, \theta\) (\(\because\) tan \(\theta\) = \(\frac {sin \, \theta}{cos \, \theta} \))

= x sin \(\theta\) = sin \(\theta\)

= x = \(\frac {sin \, \theta}{sin \, \theta} \) = 1

Correct option is: B) 1


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