# Star

I am tasked with proving the this equality \$\$fraccos(x)1 - an(x) + fracsin(x)1 - cot(x) = sin(x) + cos(x).\$\$I"ve spent hours on it and no matter how much algebra I do, I can"t figure it out. Can some one please help me?

Note that \$ an(x)=sin(x)/cos(x)=1/cot(x)\$ and\$\$fraccos(x)1 - an(x)+ fracsin(x)1 -cot(x)=fraccos^2(x)cos(x) - sin(x)+ fracsin^2(x)sin(x) -cos(x)=fracsin^2(x)-cos^2(x)sin(x) -cos(x).\$\$ Can you take it from here?

You said you spent hours on this problem, it is possible you get confused about all these trigonometric functions. One suggestion could be khổng lồ replace \$cos(x)\$ by \$c\$ and \$sin(x)\$ by \$s\$.

Bạn đang xem: Star

is making more sense to you, even though it"s just Robert.Z"s answer written with simpler symbols, then go for this sort of reduction when you work with trigonometric formulas.

Myself for instance I always write \$c^2+s^2=1\$ instead of \$cos^2(x)+sin^2(x)=1\$, I find it easier to remember.

Xem thêm: Top 19 Con Cồ Cộ Là Gì Mới Nhất 2022, Từ Điển Tiếng Việt Cồ Cộ

\$1- cot(x)=frac sin(x) -cos(x)sin(x)\$

\$1- tan(x)=frac cos(x) - sin(x)cos(x)\$

Then we have

\$fraccos^2(x) sin(x) -cos(x)+frac sin^2(x) sin(x) -cos(x)\$

\$ =frac-cos^2(x) +sin^2(x) sin(x) -cos(x)\$=\$frac(sin(x)-cos(x))(sin(x)+cos(x)) sin(x) -cos(x)\$=\$sin(x) +cos(x)\$

note that \$\$fraccos(x)1- an(x)+fracsin(x)1-cot(x)-sin(x)-cos(x)=-cos left( x ight) an left( x ight) cot left( x ight) - an left( x ight) sin left( x ight) cot left( x ight) +cos left( x ight) an left( x ight) +sin left( x ight) cot left( x ight) \$\$ and chú ý that \$\$ an(x)cot(x)=1,cos(x) an(x)=sin(x),sin(x)cot(x)=cos(x)\$\$

Thanks for contributing an answer lớn cameraminhtan.vnematics Stack Exchange!

But avoid

Asking for help, clarification, or responding khổng lồ other answers.Making statements based on opinion; back them up with references or personal experience.

Use cameraminhtan.vnJax lớn format equations. cameraminhtan.vnJax reference.