Question

Verify the identity. (cos x/ 1+ sin x) + (1+ sin x/cos x) = 2 sec x​

Answer 1

LHS

`(cos x)/(1+ sin x) + (1+ sin x)/(cos x) \\=(cos2(x)+1+2sin(x)+sin2(x))/(cos(x)(1+sin(x)) \\= (2+2sin(x))/(cos(x)(1+sin(x))) \\\\=(2 (1 + sin(x)))/(cos(x)(1+sin(x))) \\= (2)/(cos (x)) \\= 2 sec x`

= RHS PROVED

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