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If $sin^{4}\theta + cos^{4}\theta$ = $2 sin^{2}\theta cos^{2}\theta$, $\theta$ is an acute angle, then the value of $tan\theta$ is

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If $sin^{4}\theta + cos^{4}\theta$ = $2 sin^{2}\theta cos^{2}\theta$, $\theta$ is an acute angle, then the value of $tan\theta$ is
1). 1
2). 2
3). $\sqrt{2}$
4). 0

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2 answers

2 vote
Answered by on | Votes 2 |
This question was asked some where in previous year papers of ssc, and correct answer was 1

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1 vote
Answered by on | Votes 1 |

sin4 $\theta$ + cos4 $\theta$ = 2 sin2 $\theta$. cos2$\theta$

=> sin4 $\theta$ + cos4 $\theta$– 2 sin2 $\theta$. cos2 $\theta$ = 0

=> (sin2 $\theta$ – cos2 $\theta$)2 = 0

=> sin2 $\theta$ – cos2 $\theta$ = 0

=> sin2 $\theta$ = cos2 $\theta$

= tan2 $\theta$ = 1 => tan $\theta$ = + 1

$\theta$ is acute angle..




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