Question

cos theta upon 1-tan theta + sin theta-cos theta = 1+ sin theta.cos theta

Answer 1

Step-by-step 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^@#