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find positive value of m: sin(m)+cos(m)=loge(lim(tan(x)/tan(a))1-a x->a

find positive value of m:  sin(m)+cos(m)=loge(lim(tan(x)/tan(a))1-a
                              x->a                                            

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2 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 years ago
Ans:
Sol:
sin(m) + cos(m) = \log_{e}(\lim_{x \rightarrow a}(\frac{tanx}{tana}))^{1-a}
sin(m) + cos(m) = \log_{e}(1)^{1-a} = \log_{e}1
sin(m) + cos(m) = 0
sin(A+B) = sinA.cosB + cosA.sinB
2^{1/2}sin(m+\pi /4) = 0
m + \pi /4 = n\pi; n\in I
m = n\pi - \pi /4; n\in I
For the positive values of m,
n\geq 1
Cheers!
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty
siddharth gupta
28 Points
7 years ago
the solution is to be done by taking power on tanx/tana, not  on the entire limit portion.

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