Question

sec^2theta + cos^2theta is
a) <4 b) >4 c)>= 4 d) none

Answer 1

sec^2 A + cos^2 A

•••let A = 30 °

so now ,

sec ^2 30° + cos^2 30° ---(1)

= (2 / √3)^2 + (√3 /2 )^2

= 4 /3 + 3 / 4

=( 16 + 9 /12

= 25/12 =2.08 < 4

••now check at A = 45 ° in equation (1)

(√2)^2 + (1 /√2 )^2

= (2 + 1 /2 ) = 5 /2 = 2.5> 4

••check at A =90°

(0 + infinity ) = infinity

••A = 0 °
from(1)

1 + 1 = 2 <4

hence the answer will be " (d) none " because the value of sec^2A + cos^2 A can either be > 4 or < 4 but can not be equal to 4.

hope it helps !
thank you b!