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If a2 sec2x – b2 tan2x = c2 then the
value of (sec2x + tan2x) is equal to (assume b2 ≠ a2)
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b2 − a2 +2c2 b2 + a2 -
b2 + a2 − 2c2 b2 − a2 -
b2 − a2 − 2c2 b2 + a2 -
b2 − a2 b2 + a2 + 2c2
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Correct Option: B
a2 sec2x – b2 tan2x = c2
⇒ a2 (1 + tan2x) – b2 tan2x = c2
⇒ a2 + a2tan2x – b2 tan2x = c2
⇒ a2tan2x – b2 tan2x = c2 – a2
⇒ tan2x(a2 – b2) = c2 – a2
| ⇒ tan2x = | |
| a2 – b2 |
∴ sec2x + tan2x
= 1 + tan2x + tan2x
= 1 + 2 tan2x
| = 1 + | |
| a2 – b2 |
| = | |
| a2 – b2 |
| = | |
| a2 – b2 |
| = | |
| b2 – a2 |
