Question

Assume cos (A-B) = cos A cos B + sin A sin B , find cos 15° when A = 45°, B = 30°

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Answer 1

if cos(a-b)=cosa cosb + sina sinb and we have to find cos15.

15 can be expressed as (45 - 30)

So,

=cos 15 = cos (45 - 30)

= cos45cos30 + sin45sin30

= (1/√2)(√3/2) + (1/√2)(1/2)

= √3/2√2 + 1/2√2

= (√3 + 1) / 2√2

[tex][/tex]

Answer 2

$\huge\mathtt{\fcolorbox{cyan}{black}{\pink{Answer}}}$

$\cos( \alpha - \beta ) = \cos \: \alpha \cos \: \beta \: + \sin \: \alpha \: \sin \: \beta$

$(where \: \alpha = 45 \: and \: \beta = 30) \\ = \cos(45) \cos(30) + \sin(45) \sin(30) \\ = ( \frac{1 }{ \sqrt{2} } \times \frac{ \sqrt{3} }{2} ) + (\frac{1}{ \sqrt{2} } \times \frac{ \sqrt{3} }{2}) \\ = \frac{ \sqrt{3} }{2 \sqrt{2} } + \frac{ \sqrt{3} }{2 \sqrt{2} } \\ = \frac{2 \sqrt{3} }{2 \sqrt{2} } \\ = \frac{ \sqrt{3} }{ \sqrt{2} } \\ = \fbox{\sqrt{\frac{3}{2}}}$