The simplest value of sin²x + 2 tan²x

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The simplest value of sin²x + 2 tan²x – 2 sec²x + cos²x is

1. 1
2. 0
3. - 1
4. 2

Correct Option: A

sin² x + 2 tan² x – 2 sec² x + cos²x = sin²x + cos²x – 2 sec²x + 2 tan²x
= 1 – 2 (sec²x – tan²x)
= 1 – 2 = – 1
[sec²x – tan²x = 1, sin² x + cos² x = 1]