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Grade: 12

                        

Integral 1+tan(x)tan(x+a)

9 years ago

Answers : (1)

vikas askiitian expert
509 Points
							

I = [1 + tanxtanx+a]dx

I = [1 + (sinx/cosx)(sinx+a/cosx+a)]

I = [cosx+acosx+sinx+asinx]dx/cosxcosx+a                  (using , cosacosb+sinasinb = cosa-b)

I = (cosa)dx/cosxcosx+a 

multiply divide by sina

I = cota (sina)dx/cosxcosx+a          ...............1

sina = sin[(x+a)-x] = sin(x+a)cosx - cos(x+a)sinx        ............2

putting 2 in eq 1

I = cota [ tan(x+a) - tanx]dx

I = cota [ logsec(x+a) - logsecx] + c

I = cota { log[sec(x+a)/secx] } + c

this is the required integral

approve my ans if u like it

9 years ago
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