The value of tan2 θ + cot2 θ − sec2 θ cosec2 θ is: A2 B-2 C0 D1/2 Show answer & explanationCorrect answer: BExplanationThe correct answer is Option 2 i. e. −2. tan2 θ + cot2 θ − sec2 θ cosec2 θ = tan2θ+cot2θ−(1+tan2θ)(1+cot2θ)tan^{2}\theta +cot^{2}\theta -\left ( 1+tan^{2}\theta \right )\left ( 1+cot^{2} \theta \right )tan2θ+cot2θ−(1+tan2θ)(1+cot2θ) = tan2θ+cot2θ−(1+tan2θ+cot2θ+tan2θcot2θ)tan^{2}\theta +cot^{2}\theta -\left ( 1+tan^{2}\theta +cot^{2}\theta +tan^{2}\theta cot^{2}\theta \right )tan2θ+cot2θ−(1+tan2θ+cot2θ+tan2θcot2θ) = tan2θ+cot2θ−1−tan2θ−cot2θ−tan2θcot2θtan^{2}\theta +cot^{2}\theta -1 - tan^{2}\theta -cot^{2}\theta -tan^{2}\theta cot^{2}\theta tan2θ+cot2θ−1−tan2θ−cot2θ−tan2θcot2θ = −1−tan2θcot2θ-1-tan^{2}\theta cot^{2}\theta −1−tan2θcot2θ = −1−1-1-1 −1−1 = −2-2−2