1
Question
tanθ(1−cotθ)+cotθ(1−tanθ)=(1+secθcosecθ)
tanθ(1−cotθ)+cotθ(1−tanθ)=(1+secθcosecθ)
Open in App
Solution
tan θ1−cot θ+cot θ1−tan θ=(1+sec θ cosec θ)LHS=tan θ1−cot θ+cot θ1−tan θ=tan θ1−1tan θ+1tan θ1−tan θ=tan θtan θ−1tan θ+1tan θ(1−tan θ)=tan2 θtan θ−1+1tan θ(1−tan θ)=−tan2 θ1−tan θ+1tan θ(1−tan θ)=−tan3 θ+1tan θ(1−tan θ)=13−tan3 θtan θ(1−tan θ)=(1−tan θ)(1+tan2 θ+tan θ)tan θ(1−tan θ)=1+tan2 θ+tan θtan θ=sec2 θ+tan θtan θ=sec2 θtan θ+tan θtan θ=sec2 θ×cot θ+1=1cos2 θ×cos θsin θ+1=1cos θ×1sin θ+1=sec θ cosec θ+1=RHS
tan θ1−cot θ+cot θ1−tan θ=(1+sec θ cosec θ)LHS=tan θ1−cot θ+cot θ1−tan θ=tan θ1−1tan θ+1tan θ1−tan θ=tan θtan θ−1tan θ+1tan θ(1−tan θ)=tan2 θtan θ−1+1tan θ(1−tan θ)=−tan2 θ1−tan θ+1tan θ(1−tan θ)=−tan3 θ+1tan θ(1−tan θ)=13−tan3 θtan θ(1−tan θ)=(1−tan θ)(1+tan2 θ+tan θ)tan θ(1−tan θ)=1+tan2 θ+tan θtan θ=sec2 θ+tan θtan θ=sec2 θtan θ+tan θtan θ=sec2 θ×cot θ+1=1cos2 θ×cos θsin θ+1=1cos θ×1sin θ+1=sec θ cosec θ+1=RHS
Suggest Corrections
506
Similar questions
Join BYJU'S Learning Program
Explore more
Join BYJU'S Learning Program
