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trig

OCR Question:

Prove: sec^2x + cosec^2x = 4cosec^2x

i done this so far...

cos^2x + sin^2x/ sin^2x cos^2x
1/sin^2x (1-sin^2x)
1/sin^2x - sin^4x

then wot...if its right that is..
Reply 1
Avatar for mp4489
mp4489
ok....sec^2x + cosec^2x = 4cosec^2x
1/cos^2x + 1/sin^2x = 4/sin^2x
sin^2x + cos^2x = 4cos^2x
1 = 4 cos^2 x
0.25 = cos^2x
cos x = 0.5
x = 60, 300, etc

I think this is right.....i might be interpreting the thing wrong though. Do you mean cos squared x and etc.....nvm
Reply 2
Avatar for mp4489
mp4489
Hang on...that gets you nowhere in the proof....how did i go wrong.....
Reply 3
Avatar for sea tea
sea tea
9
you've solved the equation maybe? if you wanted to do that, just subtract a cosec2x from the LHS, then convert to tan x = + and - root 3.
Nandoz
OCR Question:

Prove: sec^2x + cosec^2x = 4cosec^2x

i done this so far...

cos^2x + sin^2x/ sin^2x cos^2x
1/sin^2x (1-sin^2x)
1/sin^2x - sin^4x

then wot...if its right that is..

sec^2x + cosec^2x
= 1/cos^2x + 1/sin^2x
= (cos^2x+sin^2x)/sin^2x.cos^2x
= 1/(sin^2x.cos^2x)
= 1/(0.5sin2x)^2
= 1/0.25sin^2(2x)
= 4cosec^2(2x)
Reply 5
Avatar for 7589200
7589200
18
sec^2 x + cosec^2 x = 4cosec^2 (2x)

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