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

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

Question Image
Grade:12th pass

2 Answers

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

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