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प्रश्न
If `y = log tan (π/4 + x/2)`, then prove that `(dy)/(dx) - secx = 0`.
सिद्धांत
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उत्तर
`y = log tan (π/4 + x/2)`
Differentiating with respect to x:
`(dy)/(dx) = 1/(tan(π/4 + x/2)) xx sec^2 (π/4 + x/2) xx 1/2`
= `(cos(π/4 + x/2))/(sin(π/4 + x/2)) xx 1/(cos^2(π/4 + x/2)) xx 1/2`
= `1/(2sin(π/4 + x/2) cos(π/4 + x/2))`
= `1/(sin(π/2 + x)`
= `1/cosx`
= sec x
`(dy)/(dx) - sec x = 0`
Hence proved.
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