Question

if cos theta is equal to 2 upon 3 find the value of 2 sec square theta + 2 tan square theta minus 9

Answer 1

here is your answer in above attachment

Answer 2

Heya,

Let theta be 'A'

Given=> cosA = 2/3
= base/hypotenous

Perpendicular = √(3)² - (2)²
= √9 - 4
= √5

secA = hypotenous/base = 3/2
tanA = perpendicular/base
= √5/2

So,
=> 2sec²A + 2tan²A - 9
=> 2(3/2)² + 2(√5/2)² - 9
=> (2×9)/4 + (2×5)/4 - 9
=> 9/2 + 5/2 - 9
=> (9 + 5)/2 - 9
=> 14/2 - 9
=> 7 - 9
=> -2. ..... Answer

Hope this helps....:)