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If cos4θ – sin4θ = 1 , then the value of tan2θ is 3
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1 2 -
1 3 -
1 4 -
1 5
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Correct Option: A
cos2θ + sin2θ = 1 ..... (i)
| ∴ cos4θ − sin4θ = | |
| 3 |
| ⇒ (cos2θ + sin2θ)(cos2θ − sin2θ) = | |
| 3 |
| ⇒ cos2θ − sin2θ = | ..... (ii) | |
| 3 |
By equations (i) + (ii),
| 2cos2θ = 1 + | = | ||
| 3 | 3 |
| ⇒ cos2θ = | |
| 3 |
From equation (i),
| + sin2θ = 1 | |
| 3 |
| ⇒ sin2θ = 1 − | = | ||
| 3 | 3 |
| ∴ tan2θ = | = | ||
| 2/3 | 2 |
