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

Vikas TU
14149 Points
one year ago
Dear student
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
Vikas TU
14149 Points
one year ago
Hiii in accordance to above question ,
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