Question

If 15tan² theta+4sec² theta=23, then find the value of (sec theta+cosec theta)²−sin² theta.

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

=> 15tan²A + 4sec²A = 23

=> 15tan²A + 4(1 + tan²A) = 23

=> 15tan²A + 4 + 4tan²A = 23

=> 19tan²A = 23 - 4 = 19

=> 19tan²A = 19

=> tan²A = 1 → tanA = 1 → tanA =tan45°

=> A = 45°

Hence,

(secA + cosecA)² - sin²A

(sec45° + cosec45°) - sin²45°

(√2² + √2²) - (1/√2)²

(2 + 2) - 1/2

4 - 1/2

7/2