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Vanyuwa [196]
3 years ago
6

Verify the identity. cosine of x divided by quantity one plus sine of x plus quantity one plus sine of x divided by cosine of x

equals two times secant of x.
Mathematics
1 answer:
DanielleElmas [232]3 years ago
3 0
Cos(x)/(1+sin(x) + (1+sin(x))/cos(x)=

cos²(x)/cos(x)(1+sin(x)) + (1+sin(x))²/cos(x)(1+sin(x))=

cos²(x)+1+2sin(x)+sin²(x) /cos(x)(1+sin(x))=

2+2sin(x) / cos(x)(1+sin(x))=

2(1+sin(x)) / cos(x)(1+sin(x))=

2/cos(x)=

2*sec(x)
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\bf \qquad \qquad \textit{double proportional variation}
\\\\
\begin{array}{llll}
\textit{\underline{y} varies directly with \underline{x}}\\
\textit{and inversely with \underline{z}}
\end{array}\implies y=\cfrac{kx}{z}\impliedby 
\begin{array}{llll}
k=constant\ of\\
\qquad  variation
\end{array}\\\\
-------------------------------\\\\

\bf \textit{\underline{y} varies directly as (x+3) and inversely as (x-3)}\implies y=\cfrac{k(x+3)}{x-3}
\\\\\\
\textit{we also know that }
\begin{cases}
y=21\\
x=4
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\\\\\\
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