Question

prove that sec squared theta + cosec squared theta is equals to sec square theta multiply cosec squared theta

Answer 1

$\underline{\textsf{To prove:}}$

$\mathsf{sec^2\theta+cosec^2\theta=sec^2\theta\,cosec^2\theta}$

$\underline{\textsf{Solution:}}$

$\textsf{Consider,}$

$\mathsf{sec^2\theta+cosec^2\theta}$

$\mathsf{=\dfrac{1}{cos^2\theta}+\dfrac{1}{sin^2\theta}}$

$\mathsf{=\dfrac{sin^2\theta+cos^2\theta}{cos^2\theta\,sin^2\theta}}$

$\mathsf{=\dfrac{1}{cos^2\theta\,sin^2\theta}}$

$\mathsf{=\dfrac{1}{cos^2\theta}{\times}\dfrac{1}{sin^2\theta}}$

$\mathsf{=sec^2\theta{\times}cosec^2\theta}$

$\implies\boxed{\mathsf{sec^2\theta+cosec^2\theta=sec^2\theta\,cosec^2\theta}}$

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Answer 2

Step-by-step explanation:

cosec²theta+sec² theta=cosec²theta sec² theta

answer:

cosec theta=1/sin theta

sec theta=1/cos theta

prove:

cosec²theta+sec²theta

1/sin² theta×1/cos² theta

cos²theta +sin²theta/sin²theta ×cos²theta

sec²theta×cosec²theta

hence proved