Question

please answer my question immediately

Answer 1

HELLO DEAR,

i am taking x instead of theta,,

GIVEN:-

15tan²x + 4sec²x = 23

15(sec²x - 1) + 4sec²x = 23
[ tan²x + 1 = sec²x]

15sec²x - 15 + 4sec²x = 23

19sec²x = 23 + 15

19sec²x = 38

sec²x = 38/19

sec²x = 2

secx = √2

secx = sec45°

x = 45°

so, cosecx = cosec45° = √2
we know sinx = 1/cosecx
so, sinx = 1/√2

now, (secx + cosecx)² - sin²x

= (√2 + √2)² - (1/√2)²

= (2√2)² - (1/√2)²

= 8 - 1/2

= (16 - 1)/2

= 15/2

I HOPE ITS HELP YOU DEAR,
THANKS