Solve `cosx/(1 +sinx) + (1 +sinx)/cosx = 2/cosx`

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The equation to be solved is: `cosx/(1 +sinx) + (1 +sinx)/cosx = 2/cosx`

It is seen that:

`cosx/(1 +sinx) + (1 +sinx)/cosx`

=> `(cos^2x + (1 + sinx)^2)/((1 +sin x)*cos x)`

=> `(cos^2x + 1 + sin^2x + 2*sin x)/((1 +sin x)*cos x)`

=> `(1 + 1 + 2*sin x)/((1 +sin x)*cos x)`

=> `(2*(1 + sin x))/((1 +sin x)*cos x)`

=> `2/cos x`

The equation `cosx/(1 +sinx) + (1 +sinx)/cosx = 2/cosx` is an identity and is true for all values of x.

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