Question

if sin theta=3/4 find √cosec^2-√cot^2/√sec^2-√1​

Answer 1

Hey Pretty Stranger!

Here, we've :

• 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

→ (B)² = 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

$\sf \: This \: is \: the \: required \: answer!$