How do you find a numerical value of one trigonometric function of x given $\frac{1 + cos x}{sin x} + \frac{sin x}{1 + cos x} = 4$ $(1+cosx)/sinx+sinx/(1+cosx)=4$ ?

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Answer 1 · 2016-11-12T10:00:20

$:.x=pi/6 +2pin or x=(5pi)/6 +2pin$

$(1+cosx)/sinx + sinx/(1+cosx)=4$

$((1+cosx)(1+cosx) + sinxsinx)/((1+cosx)sinx)=4$

$(1+2cosx+cos^2x+ sin^2x)/((1+cosx)sinx)=4$

$(1+2cosx+1)/((1+cosx)sinx)=4$

$(2+2cosx)/((1+cosx)sinx)=4$

$(2(1+cosx))/((1+cosx)sinx)=4$

$(2cancel(1+cosx))/(cancel(1+cosx)sinx)=4$

$2/sinx=4$

$2=4sinx$

$2/4=sinx$

$1/2=sinx$

$sin^-1(1/2)=x$

$:.x=pi/6 +2pin or x=(5pi)/6 +2pin$

How do you find a numerical value of one trigonometric function of x given (1+cosx)/sinx+sinx/(1+cosx)=41+cosxsinx+sinx1+cosx=4(1+cosx)/sinx+sinx/(1+cosx)=4?