Find the value of theta, if, Cos (theta) / 1 - sin (theta) + cos (theta) / 1 + sin (theta) = 4 ?

2 Answers
Mar 2, 2018

#theta=pi/3# or #60^@#

Explanation:

Okay. We've got:

#costheta/(1-sintheta)+costheta/(1+sintheta)=4#

Let's ignore the #RHS# for now.

#costheta/(1-sintheta)+costheta/(1+sintheta)#

#(costheta(1+sintheta)+costheta(1-sintheta))/((1-sintheta)(1+sintheta))#

#(costheta((1-sintheta)+(1+sintheta)))/(1-sin^2theta)#

#(costheta(1-sintheta+1+sintheta))/(1-sin^2theta)#

#(2costheta)/(1-sin^2theta)#

According to the Pythagorean Identity,

#sin^2theta+cos^2theta=1#. So:

#cos^2theta=1-sin^2theta#

Now that we know that, we can write:

#(2costheta)/cos^2theta#

#2/costheta=4#

#costheta/2=1/4#

#costheta=1/2#

#theta=cos^-1(1/2)#

#theta=pi/3#, when #0<=theta<=pi#.

In degrees, #theta=60^@# when #0^@<=theta<=180^@#

Mar 2, 2018

#rarrcosx=1/2#

Explanation:

Given, #rarrcosx/(1-sinx)+cosx/(1+sinx)=4#

#rarrcosx[1/(1-sinx)+1/(1+sinx)]=4#

#rarrcosx[(1+cancel(sinx)+1cancel(-sinx))/((1-sinx)*(1+sinx)]]=4#

#rarr(2cosx)/(1-sin^2x)=4#

#rarrcosx/cos^2x=2#

#rarrcosx=1/2#