Question

(Cosec2 Q-1) (sec Q+1)(secQ-1)=1

Answer 1

Answer:

LHS,

( cosec²∅ -1) ( sec∅ +1)( sec∅- 1)

= ( cosec²∅ -1)( sec²∅ -1)

= cot²∅ × tan²∅

= ( cot∅tan∅)²

= 1²

= 1

Step-by-step explanation:

identities used

1.cosec ²∅ - cot²∅ = 1

2. sec²∅ - tan²∅ = 1

and

3. tan∅ × cot∅ = 1

and

4. ( a + b)( a- b) = a² - b²

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Answer 2

Answer:

$l.h.s. \\ \\ \\ \implies( { \cosec}^{2}\theta - 1)( \sec\theta + 1)( \sec\theta - 1) \\ \\ \\ \implies({\cosec}^{2}\theta)( { \sec}^{2}\theta - {1}^{2}) \\ \\ \\ \implies({\cosec}^{2}\theta)( { \sec}^{2}\theta - 1) \\ \\ \\ \implies( { \cot}^{2}\theta)( { \tan}^{2}\theta) \\ \\ \\ \implies( { \cot\theta \tan\theta ) }^{2} \\ \\ \\ \implies {1}^{2} = 1 \\ \\ \\ hence \: l.h.s. = r.h.s.$