Math, asked by vsrinivas1969, 13 days ago

how to solve this question​

Attachments:

Answers

Answered by vipashyana1
0

\huge{\mathfrak{Answer:-}} \\ \bold{(cos \: 0° + sin \: 45° + sin \: 30°)(sin \: 90° - cos \: 45° + cos \: 60°)} \\  = (1 +  \frac{1}{ \sqrt{2}}  +  \frac{1}{2} )(1 -  \frac{1}{ \sqrt{2} }  +  \frac{1}{2} ) \\  =  {(1)}^{2}  -  {( \frac{1}{ \sqrt{2} } +  \frac{1}{2}  )}^{2}  \\  = 1 - [ {( \frac{1}{ \sqrt{2} } )}^{2} +   {( \frac{1}{2} )}^{2} + 2( \frac{1}{ \sqrt{2} })( \frac{1}{2} )  ] \\  = 1 - ( \frac{1}{2}  +  \frac{1}{4}  +  \frac{1}{ \sqrt{2} } ) \\  = 1 -  \frac{2 + 1 + 2 \sqrt{2} }{4}  \\  = 1 -  \frac{3 + 2 \sqrt{2} }{4}  \\  =  \frac{4 - (3 + 2 \sqrt{2} )}{4}  \\  =  \frac{4 - 3 - 2 \sqrt{2} }{4}  \\  =  \frac{1 - 2 \sqrt{2} }{4}  \\ \boxed{\boxed{\bold{\large{(cos \: 0° + sin \: 45° + sin \: 30°)(sin \: 90° - cos \: 45° + cos \: 60°) =  \frac{1 - 2 \sqrt{2} }{4} }}}}

Similar questions