Question

if sintheta =3/4, find the value of ✓cosec^2 - cot^2theta/sec^2theta -1

Answer 1

Hi ,

Here I am using A instead of theta.

SinA = 3/4 ----( 1 )

cosecA = 4/3 --- ( 2 )

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We know the trigonometric identity

1 ) cosec² A - cot² A = 1

2 ) sec² A - 1 = tan² A

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Value of √[(cosec²A-cot² A )/(sec² A-1)]

= √( 1/tan² A )

= √cot² A

=√ cosec² A - 1

= √( 4/3 )² - 1

= √16/9 - 1

= √( 16 - 9 )/9

= √(7/9)
= (√7 )/3

I hope this helps you.

: )

Answer 2

Hii friend,

Sin theta = 3/4 = P/H

P = 3 , H = 4

By pythagoras theroem,

(H)² = (B)²+(P)²

(4)² = (B)² + (3)²

(B)² = (4)² - (3)²=> 16-9 => 7

B= ✓7

Cosec theta = H/P = 4/3

Sec theta = H/B = 4/✓7

Cot theta = B/P = ✓7/3

Therefore,

✓Cosec²-Cot² theta/Sec² theta -1 = ✓(4/3)² - (✓7/3)² / (4/✓7)² - 1

=>✓(4/3)² - (✓7/3)²/(4/✓7)² -1

=> ✓16/9-7/9 ÷ 16/7-1

=> ✓16-7/9 ÷ 16-7/7

=> ✓9/9/9/7

=> ✓9/✓9/✓9/✓7

=> 3/3/3/✓7

=> 3/3 × ✓7/3

=> ✓7/3....Ans...

HOPE IT WILL HELP YOU..... :-)