Question

if 15tan2theta + 4sec2theta =32, find the value of (sec theta + cosec theta) 2= sin2theta
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Answer 1

Step-by-step explanation:

GIVEN: 15 tan² x + 4sec²x = 23

TO FIND: ( sec x+ cosec x)² - sin²x = ?

Since, tan² x + 1 = sec²x ( fundamental identity)

=> tan² x = sec²x -1

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

= (2√2)² - 1/2

= 8 - 1/2

= 15/2