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Cot square theta minus cosec square theta =-1.... true /false |
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Answer» Answer: Answer: 1+\frac{COT^{2}\theta}{1+cosec\theta}=cosec\theta1+1+cosecθcot2θ=cosecθ Step-by-step explanation: LHS = 1+\frac{cot^{2}\theta}{1+cosec\theta}LHS=1+1+cosecθcot2θ =1+\frac{cosec^{2}\theta-1}{cosec\theta+1}=1+cosecθ+1cosec2θ−1 /* we know the Trigonometric IDENTITY: cot²A = cosec²A-1 */ =1+\frac{(cosec\theta+1)(cosec\theta-1)}{(cosec\theta+1)}=1+(cosecθ+1)(cosecθ+1)(cosecθ−1) /*By algebraic identity: a²-b² = (a+b)(a-b) */ \begin{lgathered}=1+cosec\theta-1\\=cosec\theta\\=RHS\end{lgathered}=1+cosecθ−1=cosecθ=RHS 1+\frac{cot^{2}\theta}{1+cosec\theta}=cosec\theta1+1+cosecθcot2θ=cosecθ |
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