Question

prove that (tan theta+sec theta-1)×(tan theta+1+sec theta)=2sin theta/ 1-sin theta

Answer 1

Sin theta/cos theta+ 1/cos theta- 1/1- 1/cos theta+ sin theta/ cos theta=Sin theta-( cos theta- 1)/ Sin theta+ (cos theta-1)X Sin theta-(cos theta- 1)/ sin theta- (cos theta-1)=Sin^2 theta+ cos^2 theta+1-2cos theta-2sin theta(cos theta-1)/Sin^2 theta- cos^2theta-1+2cos theta=2-2cos theta-2sin theta•cos theta+ 2 sin theta/ Sin^2 theta- cos^2theta-sin^2theta-cos^2theta+2cos theta=2(1-cos theta)+ 2sin theta(1-cos theta)/2cos theta- 2 cos^2 theta=(1-cos theta)•(2+2sin theta)/2cos theta•(1-cos theta)=2(1+sin theta)/2cos theta=1+sin theta/cos theta=RHS
HENCE PROVED