Differential Calculus> QUESTION : Differentiate with respect to ...

QUESTION : Differentiate with respect to x.ANSWER :COSECXHow to do this..plz help What we should do either use log formula or any other ??

INDERJEET , 5 Years ago

Grade 12

3 Answers

Arun

Last Activity: 5 Years ago

Dear student

First solve 1 – cos x / 1 + cos x = 2 sin^2 (x/2) / 2 cos^2 (x/2)

expression becomes = log(tanx/2)

now on differentiation = cosx

Samyak Jain

Last Activity: 5 Years ago

1 – cosx = 2 sin² (x/2) and 1 + cosx = 2 cos² (x/2)

So, (1 – cosx) / (1 + cosx) = tan² (x/2)

Expression becomes log $\sqrt{tan^2 (x/2))}$ = log(tan(x/2))

d{log(tan(x/2))}/dx = {1/tan(x/2)} sec²(x/2) . (1/2) = 1 / 2sin(x/2) cos(x/2)

= 1 / sinx = cosecx.

Raj

Last Activity: 5 Years ago

1 - cosx = 2sin^2 (x/2) and 1 + cos x= 2 cos^ 2(x/2)

So, (1 - cosx) / (1 + cosx)= tan^ 2(x/2)

Then we got log√tan^2(x/2) = log(tan(x/2))

Then diff. W.R.T x

We get 1/ sin x = cosec x

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Differential Calculus> QUESTION : Differentiate with respect to ...

QUESTION : Differentiate with respect to x.ANSWER :COSECXHow to do this..plz help What we should do either use log formula or any other ??

INDERJEET , 5 Years ago

Arun

Samyak Jain

Raj

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