Question

cos square 45-cos square 30=x.cos 45. sin 45, x=?

Answer 1

Answer:

answer for the given problem is given

Answer 2

$\displaystyle\sf{\longrightarrow{cos^2(45)= (\frac{1}{\sqrt2})^2 = \bold{\frac{1}{2}}}$

$\displaystyle\sf{\longrightarrow{cos^2(30)=(\frac{\sqrt3}{2})^2 = \bold{\frac{3}{4}}$

$\displaystyle\sf{\longrightarrow{cos(45)=\bold{\frac{1}{\sqrt2}}$

$\displaystyle\sf{\longrightarrow{sin(45)=\bold{\frac{1}{\sqrt2}}$

Given,

$\displaystyle\sf{cos^2(45)-cos^2(30)=x\:.\:cos(45)\:.\:sin(45)$

$\displaystyle\sf{\implies\frac{1}{2}-\frac{3}{4}=x\:.\:\frac{1}{\sqrt2}\:.\:\frac{1}{\sqrt2}$

$\displaystyle\sf{\implies \frac{-1}{4}=\frac{x}{2}$

$\displaystyle\sf{\implies x=\frac{-1}{2}$

$\displaystyle\sf{\boxed{\bold{ x=\frac{-1}{2}}}}$