Question

27. If sin (A + B) = sin A cos B+cos A sin B
and cos (A - B) = cos A cos B + sin Asin B,
find the values of (i) sin 75º and (ii) cos 15°​

Answer 1

Answer:

you can find the value by sin(45+30)=sin75

both value are known

and cos(45-30)=cos15

Answer 2

Answer:

$\sin75 = \sin(30 + 45) \\ ie \: \: \: \sin(30 + 45) = \sin(30) \cos(45) + \cos(30) \sin(45 ) \\ ie \: \: \: \sin(30 + 45) = \frac{1}{2} \times \frac{1}{ \sqrt{2} } + \frac{ \sqrt{3} }{2} \times \frac{1}{ \sqrt{2} } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \: \frac{1 + \sqrt{3} }{2 \sqrt{2} } \\ \\ \cos(15) = \cos(45 - 30) \\ ie \: \: \: \cos(45 - 30) = \cos(45) \times \cos(30) + \sin(45) \times \sin(30) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{ \sqrt{2} } \times \frac{ \sqrt{3} }{2} + \frac{1}{ \sqrt{2} } \times \frac{1}{ \sqrt{2} } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{ \sqrt{3} + 1 }{2 \sqrt{2} }$