Question

Cos x/1-sin x + cosx/ 1+ sin x = 4

Answer 1

HEYA!!

How can I prove that cosx/1-sinx +cosx/1+sinx=4?

Here is the answer :

L.H.S. = cos x/(1-sin x) +cos x/(1+sin x)

=cos x[1+sin x+1-sin x]/(1-sin x).(1+sin x)

=2.cos x/(1-sin^2x)

=2.cos x/cos^2 x

= 2/cos x

Now for x=π/3 ,

L.H.S. = 2/cos (π/3)

=2/(1/2)

=2*2

=4

=R.H.S.

Question can't be proved for all value of x but only for

x = π/3 , 5π/3 , 7π/3 ,….

Equation

cos x/(1-sin x) +cos x/(1+sin x) = 4

will be satisfied.

HOPE IT WORKS!!

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