Question

Find the value of sin 15
ii) hence deduce the value of cos 75

Answer 1

SOLUTION

TO DETERMINE

The value of sin 15°

Hence deduce the value of cos 75°

EVALUATION

sin 15°

= sin ( 45° - 30° )

= sin 45° cos 30° - cos 45° sin 30°

$\displaystyle \sf{ = \frac{1}{ \sqrt{2} } \times \frac{ \sqrt{3} }{2} - \frac{1}{ \sqrt{2} } \times \frac{ 1 }{2} }$

$\displaystyle \sf{ = \frac{ \sqrt{3} - 1}{ 2\sqrt{2} } }$

Hence

cos 75°

= cos ( 90° - 15° )

= sin 15°

$\displaystyle \sf{ = \frac{ \sqrt{3} - 1}{ 2\sqrt{2} } }$

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