Question

If tan theta = 1/√3 , then evaluate ( cosec^2 theta - sec^2 theta / cosec^2 theta + sec^2 theta ) .
Plz answer it fast.

Answer 1

tan∅ = 1/√3

We know, tan30 = 1/√3

tan∅ = tan 30°

∅ = 30°

××××××××××××××××××

(cosec²∅-sec²∅)÷(cosec²∅+sec²∅)

(cosec²30-sec²30)÷(cosec²30+sec²30)

[ (2)² - (2/√3)²] ÷ [ (2)² + (2/√3)²]

=> [ 4 - 4/3] ÷ [ 4+ 4/3]

=> [ (12 - 4)/3] ÷ [ (4 + 12)/3]

=> 8 ÷ 16

=> 1/2

I hope this will help you

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Answer 2

Answer: 1/2

HOPE IT HELPS YOU