Question

Verify each trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side of the equation.

1 + sec^2x sin^2x = sec^2x

Answer 1

do you know your Pythagorean identities? you know that sec^2x will make a 1+tan^2x and evaluate the left side by writing the trig identities in variables. is how I did it. if you need me to explain more I would like an attempt from you

Answer 2

Yeah, an explanation would help. I'm confused.

Answer 3

I will show you what I have so far

Answer 4

alright. not my comment that sec^2x =1+tan^2x
now write sec^2x * sin^2x as variables where
\[\frac{ h^2 }{ a^2 }\] is secant ^2x then write out sin^2x the same way and look at them. should be very obvious

Answer 5

*note my comment

Answer 6

\[1 + \sec^2x \sin^2x\]

\[1 + (1+ \tan^2x)(1-\cos^2x)\]

This is how far I got. I don't know what you mean by h^2/a^2

Answer 7

you missing my point
\[1+\frac{ h^2 }{ a^2 }*\frac{ o^2 }{ h^2 }=\sec^2x\]
where
\[\sec^2x=1+\tan^2x\]
for the right side of the equation. leave the left side as the fractions.
o=opposite
a=adjacent
h=hypotenuse.
now what is special about the left side now

Answer 8

\[\frac{ h^2 }{ a^2 } * \frac{ o^2 }{ h^2 } = 1+\tan^2x\]

Answer 9

now cross out your h^2 and don't forget about the 1+ on the left side and what is o/a?

Answer 10

\[\tan^2x ?\]

Answer 11

yes sir, why the question? this seems so fundamental

Answer 12

the question mark after the tanx comment

Answer 13

well, Is this writing a proof?

Answer 14

not rigorously, but you just said verify the equation. This process should do jjust fine for these purposes. if you want a rigorous proof. im the wrong dude to be asking.

Answer 15

Okay, that's fine. Thanks for responding! :)

Answer 16

no problem.