Question

tat sec square theta + cosec square theta =sec square theta multiplied cosec square theta​

Answer 1

Answer:

here is the answer....pls see the attach file

Step-by-step explanation:

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Answer 2

$\huge\mathbb{SOLUTION:-}$

$\sf\underline{\blue{\:\:\:Given:\:\:\:}}$

$\sf sec {}^{2}\theta+cosec{}^{2}\theta=sec{}^{2}\theta\times cosec{}^{2}\theta$

$\sf\underline{\pink{\:\:\: \:\:\:Solution\:\:\:\:\:\:}}$

$\bullet \sf{ we\:know\:that:-}$

$\sf sec\theta=\dfrac{1}{cos\theta}\\ \\ \sf cosec\theta=\dfrac{1}{sin\theta}$

$\sf\underline{\red{\:\:\:A.T.Q\:\:\:\:}}$

$\sf sec{}^{2}\theta=\dfrac{1}{cos{}^{2}\theta}\\ \\ \sf and\:\: cosec{}^{2}\theta=\dfrac{1}{sin{}^{2}\theta}$

• L.H.S

$\sf\implies sec{}^{2}\theta+cosec{}^{2}\theta\\ \\ \sf\implies \dfrac{1}{cos{}^{2}\theta}+\dfrac{1}{sin{}^{2}\theta}\\ \\ \sf\implies \dfrac{cos{}^{2}\theta+sin{}^{2}\theta}{sin{}^{2}\theta.cos{}^{2}\theta}\\ \\ \sf{\blue{ :\:\: sin{}^{2}\theta+cos{}^{2}\theta=1}}\\ \\ \sf\implies \dfrac{1}{cos{}^{2}\theta.sin{}^{2}\theta}\\ \\ \sf\implies \:or\: \dfrac{1}{cos{}^{2}\theta}\times \dfrac{1}{sin{}^{2}\theta}\\ \\ \sf\implies sec{}^{2}\theta.csc{}^{2}\theta\\ \\ \sf\implies sec{}^{2}\theta.cosec{}^{2}\theta=sec{}^{2}\theta.cosec{}^{2}\theta$

$\sf \:\:\:L.H.S=R.H.S$