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Question Number 205403 by BaliramKumar last updated on 20/Mar/24

Answered by Rajpurohith last updated on 20/Mar/24

$$Clearly{\cot }^2\left(A\right)(1+{\cot }^2\left(A\right))=1$$$$i.e,{\cot }^2\left(A\right)\left({\mathrm{cosec}}^2\left(A\right)\right)=1$$$$\Rightarrow \frac{{\cos }^2\left(A\right)}{{\sin }^4\left(A\right)}=1$$$$or{\cos }^2\left(A\right)={\sin }^4\left(A\right)={(1-{\cos }^2\left(A\right))}^2$$$$or{cos}^2\left(A\right)=1+{\cos }^4\left(A\right)-2{cos}^2\left(A\right)$$$$\Rightarrow {cos}^4\left(A\right)-3{cos}^2\left(A\right)=-1$$$$$$

Commented by BaliramKumar last updated on 20/Mar/24

$$\mathrm{thanks}$$

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