sin cos tan?

Question

how do i figure this out

sinx/cscx + cosx/secx = sinx cscx

i've tried turning csc into 1/sin & sec into 1/cos but that got me to sin^2x & cos^2x to get 1. i don't kno where i went wrong but i need some help with that one!


one more i have is 2sin^2x - 1 = tanx -cotx/tanx+cotx.

i've tried switching the sin^2x to 1-cos^2x but i don't kno how i would get tan & cot.


if someone can showme how to work these problems out i'd appreciate it so much

Answer 1

The main thing to remember is the basic identity,
sin^2 x + cos^2 x = 1 for all x.
So, for the first one, rewriting csc x as 1/sin x and sec x as 1/cos x will get you straight to this identity:
sin x / csc x + cos x / sec x = sin x csc x
<=> sin x / (1/sin x) + cos x (1/cos x) = sin x (1/sin x)
<=> sin x (sin x) + cos x (cos x) = sin x / sin x
<=> sin^2 x + cos^2 x = 1
<=> 1 = 1, which is true. 8-)

For the second, it's usually a good idea to start with the more complex side and simplify it:
RHS = (tan x - cot x) / (tan x + cot x)
= (sin x / cos x - cos x / sin x) / (sin c / cos x + cos x / sin x)
Multiply top and bottom by sin x cos x:
= (sin^2 x - cos^2 x) / (sin^2 x + cos^2 x)
= (sin^2 x - cos^2 x) / 1
Now use cos^2 x = 1 - sin^2 x:
= sin^2 x - (1 - sin^2 x)
= 2 sin^2 x - 1.

Answer 2

while dealing with the sin, cos, tan, csc, sec, and cot, it extremely is least perplexing to do not forget in case you comprehend "sohcahtoa." you will see what "sohcahtoa" ability in a 2d. while dealing with a triangle, it extremely is maximum sturdy to discover the place theta is. depending on the place theta is on the triangle determines which trig function you employ. sin= opposite/hyponetuse cos= adjoining/hypotenuse tan= opposite/adjoining csc= hypotenuse/opposite sec= hypotenuse/adjoining cot= adjoining/opposite After looking theta, you will discover which edge of the triangle is the hypotenuse, opposite edge, and adjoining edge. They hypotenuse is the longest edge of the triangle (in perfect triangles). opposite would properly be got here upon straight away throughout (diagnally) from theta. adjoining would properly be got here upon perfect next to theta. desire this facilitates. :)