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सिद्ध कीजिए कि `(cosx)/((1-sinx))=tan((pi)/(4)+(x)/(2))`

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बायाँ पक्ष `=(cosx)/(1-sinx)=(cos^(2)x//2-sin^(2)x//2)/(1-2sinx//2cosx//2)`
`=(cos^(2)x//2-sin^(2)x//2)/((cos^(2)x//2+sin^(2)x//2)-(2sinx//2cosx//2))`
`=((cosx//2-sinx//2)(cosx//2+sinx//2))/((cosx//2-sinx//2)^(2))`
`=((cosx//2+sinx//2))/((cosx//2-sinx//2))=(cosx//2(1+(sinx//2)/(cosx//2)))/(cosx//2(1-(sinx//2)/(cosx//2)))`
`=(1+tanx//2)/(1-tanx//2)=(tanpi//4+tanx//2)/(1-tanpi//4 tan x//2)" "(because tan.(pi)/(4)=1)`
`=tan((pi)/(4)+(x)/(2))=` दायाँ पक्ष

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