Question

if theta is an acute angle and Cos theta + sin theta by cos theta minus sin theta is equal to 1 + root 3 by 1 minus root 3 find the value of 2 sec squared theta minus 3 cosec squared theta

Answer 1

Let theta=p, cp=cosp and sp=sinp.
(cp+sp)/(cp-sp)=(1+sqrt(3))/(1-sqrt(3));
cp-sqrt(3)cp+sp-spsqrt(3)=cp+cpsqrt(3)-sp-spsqrt(3);
2sp=2cpsqrt(3);
sp=cpsqrt(3);
tanp=sqrt(3);
Now p<pi/2;
Hence p=60° or theta=pi/3;