naresh bought 4 dozen pencils at rs 10.80 a dozen and sold them for 80 paise each find the gain or loss parsent
Answers
Answer:
urAnswer:
sin
2
(x)−cos
2
(x)
sin
4
(x)−cos
4
(x)
=1
\color{yellow} {\Huge {\sf{Solution:}}}Solution:
\color{blue} {\large {\bf{Factor\:\sin ^4(x)-\cos ^4(x)}}}Factorsin
4
(x)−cos
4
(x)
\tt \color{blue} {\mathrm{Rewrite\:}\sin ^4(x)-\cos ^4(x)\mathrm{\:as\:}(\sin ^2(x))^2-(\cos ^2(x))^2=(\sin ^2(x))^2-(\cos ^2(x))^2}Rewritesin
4
(x)−cos
4
(x)as(sin
2
(x))
2
−(cos
2
(x))
2
=(sin
2
(x))
2
−(cos
2
(x))
2
\color{fuchsia} {\normalsize {\mathrm{Apply\:exponent\:rule}:\quad \:a^{bc}=(a^b)^c}}Applyexponentrule:a
bc
=(a
b
)
c
\color{fuchsia} {\normalsize \sin ^4(x)=(\sin ^2(x))^2}sin
4
(x)=(sin
2
(x))
2
\color{fuchsia} {\normalsize =(\sin ^2(x))^2-\cos ^4(x)}=(sin
2
(x))
2
−cos
4
(x) =
\color{fuchsia} {\normalsize \mathrm{Apply\:exponent\:rule}:\quad \:a^{bc}=(a^b)^c}Applyexponentrule:a
bc
=(a
b
)
c
\color{fuchsia} {\normalsize \cos ^4(x)=(\cos ^2(x))^2}cos
4
(x)=(cos
2
(x))
2
\color{fuchsia} {\normalsize =(\sin ^2(x))^2-(\cos ^2(x))^2}=(sin
2
(x))
2
−(cos
2
(x))
2
=
\mathrm{Apply\:Difference\:of\:Two\:Squares\:Formula:\:}ApplyDifferenceofTwoSquaresFormula: x^2-y^2=(x+y)(x-y)
(\sin ^2(x))^2-(\cos ^2(x))^2=(\sin ^2(x)+\cos ^2(x))(\sin ^2(x)-\cos ^2(x))(sin
2
(x))
2
−(cos
2
(x))
2
=(sin
2
(x)+cos
2
(x))(sin
2
(x)−cos
2
(x))
=(\sin ^2(x)+\cos ^2(x))(\sin ^2(x)-\cos ^2(x))(sin
2
(x)+cos
2
(x))(sin
2
(x)−cos
2
(x)) =
\color{blue} {\large {\bf{Factor\:\sin ^2(x)-\cos ^2(x)}}}Factorsin
2
(x)−cos
2
(x)
\mathrm{Apply\:Difference\:of\:Two\:Squares\:Formula:\:}ApplyDifferenceofTwoSquaresFormula: x^2-y^2=(x+y)(x-y)
\sin ^2(x)-\cos ^2(x)=(\sin (x)+\cos (x))(\sin (x)-\cos (x))sin
2
(x)−cos
2
(x)=(sin(x)+cos(x))(sin(x)−cos(x))
(x)=(sin(x)+cos(x))(sin(x)−cos(x))
=(\sin (x)+\cos (x))(\sin (x)-\cos (x))=(sin(x)+cos(x))(sin(x)−cos(x))
\large=(\sin ^2(x)+\cos ^2(x))(\sin (x)+\cos (x))(\sin (x)-\cos (x)) < /p > < p > (x))(sin(x)+cos(x))(sin(x)−cos(x)) < /p > < p > \large =\frac{(\sin ^2(x)+\cos ^2(x))(\sin (x)+\cos (x))(\sin (x)-\cos (x))}{\sin ^2(x)-\cos ^2(x)}=(sin
2
(x)+cos
2
(x))(sin(x)+cos(x))(sin(x)−cos(x))</p><p>(x))(sin(x)+cos(x))(sin(x)−cos(x))</p><p>=
sin
2
(x)−cos
2
(x)
(sin
2
(x)+cos
2
(x))(sin(x)+cos(x))(sin(x)−cos(x))
=
\mathrm{Apply\:Difference\:of\:Two\:Squares\:Formula:\:}ApplyDifferenceofTwoSquaresFormula: x^2-y^2=(x+y)(x-y)
\sin ^2(x)-\cos ^2(x)=(\sin (x)+\cos (x))(\sin (x)sin
2
(x)−cos
2
(x)=(sin(x)+cos(x))(sin(x)
(x)=(sin(x)+cos(x))(sin(x)−cos(x)) < /p > < p > =\frac{(\sin ^2(x)+\cos ^2(x))(\sin (x)+\cos (x))(\sin (x)-\cos (x))}{(\sin (x)+\cos (x))(\sin (x)-\cos (x))}(x)=(sin(x)+cos(x))(sin(x)−cos(x))</p><p>=
(sin(x)+cos(x))(sin(x)−cos(x))
(sin
2
(x)+cos
2
(x))(sin(x)+cos(x))(sin(x)−cos(x))
=
\mathrm{Cancel\:}\frac{(\sin ^2(x)+\cos ^2(x))(\sin (x)+\cos (x))(\sin (x)-\cos (x))}{(\sin (x)+\cos (x))(\sin (x)-\cos (x))}:\quad \sin ^2(x)+\cos ^2(x)Cancel < /p > < p > (sin(x)+cos(x))(sin(x)−cos(x))Cancel
(sin(x)+cos(x))(sin(x)−cos(x))
(sin
2
(x)+cos
2
(x))(sin(x)+cos(x))(sin(x)−cos(x))
:sin
2
(x)+cos
2
(x)Cancel</p><p>(sin(x)+cos(x))(sin(x)−cos(x))
\mathrm{Cancel\:the\:common\:factor:}\:\sin (x)+\cos(x)Cancelthecommonfactor:sin(x)+cos(x)Cancelthecommonfactor:sin(x)+cos(x)Cancelthecommonfactor:
Answer:
cost of 12 pencil is 10.80÷12=90paise
loss=90-80=10paise
loss percentage=10/80×100=12.5%
Step-by-step explanation:
hope it'll help you make it brainliest answer please please please please please please please