Question

find the value of cot 45 degree / sin 30 degree + cos 60 degree​

Answer 1

Correct Question :-

Find the value of :

• $\sf{ \dfrac{{cot \: 45}^{ \circ}}{{sin \: 30}^{ \circ} + {cos \: 60}^{ \circ}}}$

Answer :-

$\sf{ \dfrac{{cot \: 45}^{ \circ}}{{sin \: 30}^{ \circ} + {cos \: 60}^{ \circ}} = 1}$

Step-by-step explanation:

To Find :-

• The value of $\sf{ \dfrac{{cot \: 45}^{ \circ}}{{sin \: 30}^{ \circ} + {cos \: 60}^{ \circ}}}$

Solution:

$\dashrightarrow \: \sf{ \dfrac{{cot \: 45}^{ \circ}}{{sin \: 30}^{ \circ} + {cos \: 60}^{ \circ}}}$

By using the trigonometric ratio of [cot 45° = 1], We get,

$\dashrightarrow \: \sf{ \dfrac{1}{{sin \: 30}^{ \circ} + {cos \: 60}^{ \circ}}}$

By using the trigonometric ratio of [sin 30° = 1/2] and [cos 60° = 1/2] We get,

$\dashrightarrow \: \sf{ \dfrac{1}{ \dfrac{1}{2} + \dfrac{1}{2}}}$

By adding 1/2 and 1/2, We get,

$\dashrightarrow \: \sf{ \dfrac{1}{1}}$

$\sf{ \dashrightarrow \: 1}$

Hence,

$\bigstar \: \: \: \: \: \: \sf{ \dfrac{{cot \: 45}^{ \circ}}{{sin \: 30}^{ \circ} + {cos \: 60}^{ \circ}} = 1}$

Answer 2

Given,

$\frac{cot 45\° }{sin 30 \° + cos 60 \°}\\\\=\frac{1}{\frac{1}{2}+\frac{1}{2}} [\because cot 45\°= 1, sin 30 \°= cos 60 \°=\frac{1}{2}]\\\\=\frac{1}{1} = 1$$\degrees$

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