secX - tanX = cot(45-X/2
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Explanation:
RHS
tan(x2+π4)=tanπ4+tanx21−tanx2tanπ4
=1+tanx21−tanx2 = cosx2+sinx2cosx2−sinx2
Now multiply the numerator and denominator by (cosx2+sinx2)
= 1+2sinx2cosx2cos2x2−sin2x2 = 1+sinxcosx= sec x + tanx
LHS
RHS=LHS
RHS
tan(x2+π4)=tanπ4+tanx21−tanx2tanπ4
=1+tanx21−tanx2 = cosx2+sinx2cosx2−sinx2
Now multiply the numerator and denominator by (cosx2+sinx2)
= 1+2sinx2cosx2cos2x2−sin2x2 = 1+sinxcosx= sec x + tanx
LHS
RHS=LHS
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