Question

Find the value of
sin 7½°

Answer 1

½° lies in the first quadrant.

Therefore, sin 7½° is positive.

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√21√2∙√32√32 + 1√21√2∙1212

           = √32√2√32√2 + 12√212√2

           = √3+12√2√3+12√2

Again for all values of the angle A we know that, cos A = 1 - 2 sin22A2A2

⇒ 1 - cos A = 2 sin22 A2A2

⇒ 2 sin22 A2A2 = 1 - cos A

⇒ 2 sin22 7½˚ = 1 - cos 15°

⇒ sin22 7½˚ = 1−cos15°21−cos15°2

⇒ sin22 7½˚ = 1−√3+12√221−√3+12√22

⇒ sin22 7½˚ = 2√2−√3−14√22√2−√3−14√2

⇒ sin 7½˚ = 4−√6−√28−−−−−−−√4−√6−√28, [Since sin 7½° is positive]

⇒ sin 7½˚ = 4−√6−√2√2√24−√6−√22√2

Therefore, sin 7½˚ = 4−√6−√2√2√24−√6−√22√2...

thankyou

Answer 2

Hope it is useful for you .