Question

If y = logtan[tan(π/4+X/2)] Then show that dy/dx-secx = 0

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Answer 1

Step-by-step explanation:

y = logtan[π/4+x/2]

dy/dx = 1/tan(π/4+x/2) × sec²(π/4+x/2) ×1/2

=>dy/dx = 1+tan²(π/4+x/2)/2tan(π/4+x/2)

=> dy/dx = 1/2tan(π/4+x/2)/1+tan²(π/4+x/2)

=>dy/dx = 1/sin2(√/4+x/2)

=> dy/dx = 1/sin(π/2+x/2) = 1/cosx= secx

=>dy/dx = secx

so , dy/dx -secx = secx-secx= 0 proved