Question

If √3 sinƟ-cosƟ=0 and 0˚<Ɵ <90˚, find the value of Ɵ​

Answer 1

√3sin theta-cos theta=0

√3sin theta=cos theta

by squaring on both sides,

3sin²theta=cos²theta

3sin²theta-cos²theta=0

3sin²theta-(1-sin²theta)=0

3sin²theta-1+sin²theta=0

4sin²theta-1=0

4sin²theta=0+1

4sin²theta=1

sin²theta=1/4

by taking square roots on both sides,

sin theta=1/2

but given that, 0°<theta<90°

i.e.theta lies in 1st quadrant.

so, sin theta=1/2

therefore,

theta=30°

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Answer 2

Answer:

30°

Step-by-step explanation:

From the question, we can say,

√3 sinθ = cosθ.

=> √3 = cosθ/sinθ

=> √3 = cotθ [cotθ = cosθ/sinθ]

We know, cot(30) = √3

Therefore, θ = 30°

All the best, keep on solving the sample paper