(Cosec theta - cos theta)^2 = 1-cos theta upon 1 + cos theta - Maths - Introduction to Trigonometry

Question

(Cosec theta - cos theta)^2 = 1-cos theta upon 1 + cos theta

Ankita Agarwal · Accepted Answer

Dear Student,

May be your question will be cosec θ- cot θ2=1- cos θ1+ cos θTaking L
H
S⇒cosec θ- cot θ2⇒cosec2 θ+cot2 θ-2cosec θ cot θ                           a-b2=a2+b2-2ab⇒1sin2  θ+cos2 θsin2 θ -2
cos θsin θ
sin θ                                 cosec x=1sin x , cot x=cos x sin x ⇒1sin2  θ+cos2 θsin2 θ -2
cos θsin2 θ⇒1+ cos2θ- 2 cosθsin2  θ⇒1-cosθ21-cos2θ                                                                  sin2x+cos2x=1⇒1-cosθ1- cosθ1-cosθ1+cosθ                                                   a2-b2=a+ba-b⇒1-cosθ1+cosθ R
H S hence L H S =R H S proved
Regards