1 + tan 15° cot 75° is equal to:

Correct option is A

Given:

​$$1 + \tan 15^\circ \cdot \cot 75^\circ$$​​

Formula Used:

​$$1 + \tan^2 \theta =\sec^2\theta$$​​

​$$\tan (90^\circ -\theta ) =\cot\theta$$​​

Solution:

$$1 + \tan 15^\circ \cdot\tan(90^\circ - 75^\circ)$$​​

​$$=1 + \tan 15^\circ \cdot \tan 15^\circ$$​​

​$$= 1 + \tan^2 15^\circ$$​​

​$$= \sec^2 15^\circ$$​​