If 2 sec2 θ - 9 sec θ + 7 = 0, then what is the value of cos2 θ + sec2 θ ?
Answer & explanation
Correct answer: option 1
2 sec2 θ - 9 sec θ + 7 = 0
2 sec2 θ - 7 sec θ - 2 sec θ + 7 = 0
sec θ ( 2 sec θ - 7 ) - 1 ( 2 sec θ - 7 ) = 0
Either ( 2 sec θ - 7 ) = 0 or ( sec θ - 1 ) = 0
( 2 sec θ - 7 ) = 0 is not possible.
& ( sec θ - 1 ) = 0
sec θ = 1
So, θ = 0º
Now,
cos2 θ + sec2 θ
= cos2 0º + sec2 0º
= 1 + 1
= 2