Question

Prove that tan (180- theta) cosec(180+theta)-sin(90-theta) = tan theta sin theta

Answer 1

tan(180-theta)=-tan theta

cosec(180+theta)=-cosec theta

sin(90-theta)=cos theta

After putting the values we get,

=>(-tan theta)(-cosec theta)-cosec theta

=>(sin theta/cos theta ×1/sin theta)-cos theta

=> 1/cos theta- cos theta

=>1-cos^2 theta/cos theta

=>sin^2 theta/cos theta.

{sin theta/ cos theta = tan theta}

=>tan theta sin theta

Hence Proved.