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