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If $3sin\theta + 5cos\theta$ = 5, then $5sin\theta - 3cos\theta$ is equal to

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If $3sin\theta + 5cos\theta$ = 5, then $5sin\theta - 3cos\theta$ is equal to
1). $\pm 3$
2). $\pm 5$
3). 1
4). $\pm 2$

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2 answers

3 vote
Answered by on | Votes 3 |
is $\pm 3$ is the correct answer am i right

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0 vote
Answered by on | Votes 0 |

3 sin$\theta$ + 5 cos$\theta$ = 5 ...(i)
5 sin$\theta$ – 3 cos$\theta$ = x ...(ii)
On squaring and adding,
9 sin2$\theta$ = + 25 cos2$\theta$ + 25 sin2$\theta$ + 9cos2$\theta$ = 25 + x2
=> 9 (sin2$\theta$ + cos2$\theta$ ) + 25 (cos2$\theta$ +sin2$\theta$ ) = 25 + x2
=> 9 + 25 = 25 + x2
=> x2 = 9
=> x = ±3 .




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