find the value of tan 7 1/2
Answers
Answer:
Solution:
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∙√32 - 1√2∙12
= √32√2 - 12√2
= √3−12√2
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∙√32 + 1√2∙12
= √32√2 + 12√2
= √3+12√2
Now, tan 7½° = sin7½°cos7½°
= 2sin27½°2cos7½°sin7½°
= 1−cos15°sin15°
= 1−√3+12√2√3−12√2
= 2√2−√3−1√3−1
= (2√2−√3−1)(√3+1)(√3−1)(√3+1)
= 2√6−3−√3+2√2−√3−112
= √6 - √3 + √2 - 2
Therefore, tan 7½° = √6 - √3 + √2 - 2
Step-by-step explanation:
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