Question

helpppppppp please.

Answer 1

@Hero

Answer 2

What do you want to do with that?

Answer 3

Simplify the trigonometric expression. Show your work.

Answer 4

if you want to combine the two fractions, need to multiply by a common denominator

Answer 5

okay... idk how to do that?

Answer 6

\[[\frac{ 1 }{ 1+\sin \theta }+\frac{ 1 }{ 1-\sin \theta }]*\frac{ (1+\sin \theta)(1-\sin \theta) }{ (1+\sin \theta)(1-\sin \theta) }\]

Answer 7

Just multiplying the whole thing by 1... a ratio of something over itself

Answer 8

okay.. what does sin o stand for?

Answer 9

is it kinda like pi=3.14? does it stand for a number?

Answer 10

can u do it step by step and explain..

Answer 11

one sec

Answer 12

\(\bf \cfrac{1}{1+sin(\theta)}+\cfrac{1}{1-sin(\theta)}\impliedby LCD\to [1+sin(\theta)][1-sin(\theta)]
\\ \quad \\
\cfrac{(1-sin(\theta))+(1+sin(\theta))}{[1+sin(\theta)][1-sin(\theta)]}\implies
\cfrac{1\cancel{-sin(\theta)}+1\cancel{+sin(\theta)}}{[1+sin(\theta)][1-sin(\theta)]}
\\ \quad \\
----------------------------------\\
\textit{difference of squares}
\\ \quad \\
(a-b)(a+b) = a^2-b^2\qquad \qquad
a^2-b^2 = (a-b)(a+b)\qquad thus\\
----------------------------------
\\ \quad \\
\cfrac{1\cancel{-sin(\theta)}+1\cancel{+sin(\theta)}}{{\color{brown}{ [1^2-sin^2(\theta)] }}}\implies \cfrac{2}{{\color{brown}{ cos^2(\theta)}}}
\\ \quad \\
2\cdot \cfrac{1}{cos^2(\theta)}\implies 2sec^2(\theta)\)

Answer 13

the denominator is combined, since it's just a difference of squares
and keep in mind that \(\bf sin^2(\theta)+cos^2(\theta)=1\implies sin^2(\theta)={\color{brown}{ 1-cos^2(\theta)}}\)

Answer 14

woops, darn that came out off lemme redo that

Answer 15

\(\bf sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)={\color{brown}{ 1-sin^2(\theta)}}\) rather