Question

Hey.☺

50 points yrr❤❤

(sin^4-cos^4+1)cosec^2=2

Answer 1

Heyy mate ❤✌✌❤

Here's your Answer....

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L.H.S.

[sin^4 - cos^4 + 1] cosec^2

=> [ (sin^2)^2 - (cos^2)^2 + 1] cosec^2

=> [ (sin^2 + cos^2) (sin^2 - cos^2) +1] cosec^2

=> [ sin^2 - cos^2 + 1] cosec^2

=> [ sin^2 + ( 1 - cos^2) + 1 ] cosec^2

=> [ sin^2 + sin^2 ] cosec^2

=> 2 sin^2 × 1/ sin^2

=> 2.
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Answer 2

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sᴏʟᴜᴛɪᴏɴ–

$( {sin}^{4} - {cos}^{4} + 1)cosec {}^{2} = 2$
$lhs \\ (( {sin}^{2} ) {}^{2} - { {(cos}^{2} )}^{2} + 1) {cosec}^{2}$
$(( {sin}^{2} + {cos}^{2} )({sin}^{2} - {cos}^{2} ) + 1)$
${cosec}^{2}$
$(1 \times {sin}^{2} - {cos}^{2} + 1) {cosec}^{2} \\ ( {sin}^{2} + 1 - {cos}^{2} ) {cosec}^{2} \\ ( {sin}^{2} + {sin}^{2} ) \times \frac{1}{ {sin}^{2} } \\ 2 {sin}^{2} \times \frac{1}{ {sin}^{2} } \\ 2 \times 1 \\ = 2$
2= rhs

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ᴛʜᴀɴᴋs☺️