Question

Show that (1+cot 2theata) (1-cos the ta) (1+cos theta) =1​

Answer 1

$\bold\red{\underline{\underline{Answer:}}}$

$\bold\green{\underline{\underline{Proof}}}$

$\bold{L.H.S.=(1+cot^{2} \ theta)(1-cos \ theta)(1+cos \ theta)}$

$\bold{=(1+cot^{2} \ theta)(1-cos^{2} \ theta)}$

$\bold{\ (a+b)(a-b)=a^{2}-b^{2}}$

$\bold{\ (1-cos \ thita)(1+cos \ thita)=(1-cos^{2} \ thita)}$

$\bold{=(1+cot^{2} \ thita)(1-cos^{2} \ thita)}$

$\bold{1-cos^{2} \ thita=sin^{2} \ thita)}$

$\bold{\ (1-cot^{2} \ thita)=cosec^{2} \ thita}$

$\bold{=(cosec^{2} \ thita)(sin^{2} \ thita)}$

$\bold{\ cosec^{2}=\frac{1}{sin^{2} \ thita}}$

$\bold{=(\frac{1}{sin^{2} \ thita})(sin^{2} \ thita)}$

$\bold{=1}$

$\bold{=R.H.S.}$

$\bold\red{Hence, \ proved}$

$\bold\red{(1+cot^{2} \ thita)(1-cos \ thita)(1+cos \ thita)=1}$