Question

If 15 tan^2 + 45 sec^2 = 23 ,find (sec + cosec) - sin^2

Answer 1

Answer:

15/2

Step-by-step explanation:

Since, 15 tan²x + 4sec²x = 23

=> 15( sec²x -1) + 4sec²x = 23

=> 19sec²x - 15 = 23

=> 19sec² x = 38

=> sec² x = 2

=> sec x = √2 ………….(1) ( ie hypotenuse= √2, adjacent side= 1, => opposite side= 1)

=> cosec x= √2 ………… (2)

& sin x = 1/√2 ……….. (3)

So, ( secx + cosecx )² - sin² x

= ( √2 + √2)² - 1/2

= 8 - 1/2

= 15/2.

Answer 2

Please refer the image

Hope it helps <3