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anonymous
 one year ago
How do I substitute identities to make the right side match the left?
cotx sec^4x = cotx+2tanx+tan^3x
(sinx)(tanx cosxcotx cosx) = 12cos^2x
1+sec^2x sin^2x = sec^2x
(sinx/1cosx)+(sinx/1+cosx) = 2cscx
anonymous
 one year ago
How do I substitute identities to make the right side match the left? cotx sec^4x = cotx+2tanx+tan^3x (sinx)(tanx cosxcotx cosx) = 12cos^2x 1+sec^2x sin^2x = sec^2x (sinx/1cosx)+(sinx/1+cosx) = 2cscx

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.01. The key to this one is that sec^2(x) = 1 + tan^2(x). So the left side is cot(x) (1 + tan^2(x)) (1 + tan^2(x)) Expanding this term by term you get cot(x) + 2 cot(x) tan^2(x) + cot(x) tan^4(x), but since cot(x) tan(x) = 1, that turns into cot(x) + 2 tan(x) + tan^3(x), which is the same as the right side. #2. Just copying it first... (sin x)(tan x cos x  cot x cos x) = 1  2 cos^2 x (sin x)[ (sin x/cos x)(cos x)  (cos x/sin x)(cos x) ] = (1  cos^2 x)  cos^2 x (sin x) [ sin x  (cos^2 x/sin x) ] = sin^2 x  cos^2 x sin^2 x  cos^2 x = sin^2 x  cos^2 x #3. 1 + sec^2(x) sin^2(x) = sec^2(x) But sec(x) = 1/cos(x), so sec(x)sin(x) = tan(x), so the left side becomes 1 + tan^2(x) = sec^2(x) This is a wellknown Pythagorean identity. #4. Ugh! ...OK ... (sin x)/(1  cos x) + (sin x)/(1 + cos x) = 2 csc x Multiply all three terms by (1  cos x)(1 + cos x), obtaining (sin x)(1+cos x) + (sin x)(1  cos x) = 2 csc x (1  cos^2 x) But 1  cos^2 x is sin^2 x, so this becomes (sin x)(1+cos x) + (sin x)(1  cos x) = 2 csc x (sin^2 x) sin x + sin x cos x + sin x  sin x cos x = 2 sin x 2 sin x = 2 sin x #5. The righthand side is just a 1, since sec x = 1 / cos x. We have  tan^2 x + sec^2 x = 1, or sec^2 x = 1 + tan^2 x, again the wellknown Pythagorean identity.

alekos
 one year ago
Best ResponseYou've already chosen the best response.0you're not supposed to spoonfeed the answers

alekos
 one year ago
Best ResponseYou've already chosen the best response.0get'em to do a bit of work

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thank you for your help. I really appreciate the step by step, it helped me to better see what I have to do. Next time though, instead of giving me the answer please walk me or anyone else for that matter through it. It will benefit the person more than just giving them the answers. But yet again, I appreciate you doing that for me, thank you.

alekos
 one year ago
Best ResponseYou've already chosen the best response.0i'm glad you see it that way
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