Question

If 15 tan^2 A+4 sec^2 A=23, then find the value of (sec A +cosec A)^2 - sin^2 A

Asked byisha_singh(student), on 23/9/12
Answer

Answer 1

hope u get the solution

Answer 2

Answer:

15/2

Step-by-step explanation:

By Trigonometric Identity,

tan²θ + 1 = sec²θ

=> tan²θ = sec²θ - 1 --------(1)

According to the question,

15tan²θ + 4sec²θ = 23

15(sec²θ - 1) + 4sec²θ = 23 ---- from (1)

15sec²θ - 15 + 4sec²θ = 23

19sec²θ = 23 + 15

19sec²θ = 38

sec²θ = 38/19

sec²θ = 2

secθ = √2 --------(2)

→cosθ = 1/√2

sin²θ = 1 - cos²θ

sinθ = √(1 - cos²θ)

= √(1 - 1/2)

= 1/√2 --------(3)

→ cosecθ = 1/sinθ

= √2 --------(4)

Now,

(secθ + cosecθ)² - sin²θ

from (2), (3) and (4),

(√2 + √2)² - (1/√2)²

= (2√2)² - 1/2

= 8 - 1/2

= (16 - 1)/2

= 15/2

Hence, we got the answer.