What is the value of cot in the given question? Choose the answer among the given options.

7½° lies in the first quadrant.

Therefore, both sin 7½° and cos 7½° is positive.

For all values of the angle A we know that, sin (α - β) = sin α cos β - cos α sin β.

Therefore, sin 15° = sin (45° - 30°)

= 1/√2∙√3/2 - 1/√2∙1/2

= √3/2√2 - 1/2√2

= √3−1/2√2

Hope this helps 

Good luck 

Again, for all values of the angle A we know that, cos (α - β) = cos α cos β + sin α sin β.

Therefore, cos 15° = cos (45° - 30°) 
cos 15° = cos 45° cos 30° + sin 45° sin 30°
           = 1/√2∙√3/2 + 1/√2∙1/2
           = √3/2√2 + 1/2√2
           = √3+1/2√2

Now cot 7½°

= cos7½°/sin7½°

= 2cos7½°∙cos7½°/2sin7½°∙cos7½°

= 2cos^27½°/2sin7½°cos7½°

= 1+cos15°/sin15°

= 1+cos(45°−30°)/sin(45°−30°)

= 1+(√3+1/2)/2√2/(√3−1)/2√2

= 2√2+√3+1/√3−1

= (2√2+√3+1)(√3+1)/(√3−1)(√3+1)

= 2√6+2√2+3+√3+√3+1 / 3-1

= 2√6+2√2+2√3+4 / 2

= √6 + √2 + √3 + 2

= 2 + √2 + √3 + √6