# (1/cosx) + tanx = (cosx)/(1-sinx). Prove that LHS = RHS. Please help anyone?

### 2 Answers

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- 8 years agoFavorite Answer
LHS = (1 / cos x) + tan x

= (1 / cos x) + (sin x / cos x)

= (1 + sin x) / cos x

= [(1 + sin x)(1 − sin x)] / cos x (1 − sin x)

= (1 − sin² x) / cos x (1 − sin x)

= cos² x / cos x (1 − sin x)

= cos x / (1 − sin x)

= RHS

- Anonymous8 years ago
L H S

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1/cos x +tan x

RHS

cos x / (1-sin x ) * (1+sin x) / (1+sin x)

cos x (1+sin x) / (1-sin^2 x)

cos x (1+sin x) / cos^2 x

= (1+sin x ) / cos x

= 1 / cos x + sin x / cos x

1 / cos x + tan x

= L H S

so proved.

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