Question

If tan teta =1/root7 ,then cosec²teta -sec² teta /cosec²teta+sec²teta =?

Answer 1

Answer:

Hope it is helpful for you

Answer 2

Answer:-

Theta is taken as A.

Given:

Tan A = 1/√7

(Squaring on both sides)

→ tan² A = (1/√7)²

→ Sin² A/Cos² A = 1/7

→ Sin² A (1/Cos² A) = 1/7

→ Sin² A * Sec² A = 1/7

→ Sec² A = (1/7)/Sin² A

→ Sec² A = 1/(7*Sin² A).

→ Sec² A = 1/7(1/Sin² A)

→ Sec² A = Cosec² A/7 -- equation (1).

Let,

(Cosec² A - Sec² A)/Cosec² A + Sec² A = a

→ (Cosec² A - Cosec² A/7) = a(Cosec² A + Cosec² A/7)

→ (7Cosec² A - Cosec² A)/7 = a(7 Cosec² A + Cosec² A)/7

→ 6Cosec² A/7 = a(8 Cosec² A )/7

(Cosec² A/7 are cancelled out both sides)

→ 6 = 8a

→ a = 6/8

→ a = 3/4

Hence, the value of (Cosec² A - Sec² A)/(Cosec² A + Sec² A) is 3/4.