Question

what is the value of ( tan theta × cosec theta )² - ( sin theta × sec theta )²



plz answer fast​

Answer 1

Answer:

To prove:

(sinθ+cosecθ)2+(cosθ+secθ)2=7+tan2θ+cot2θ

Solution:

L.H.S. =(sinθ+cosecθ)2+(cosθ+secθ)2

=sin2θ+cosec2θ+2sinθ.cosecθ+cos2θ+sec2θ+2cosθ.secθ

=(sin2θ+cos2θ)+1+cot2θ+2+1+tan2θ+2

=1+6+tan2θ+cot2θ

=7+tan2θ+cot2θ