Question

If theta and 3theta-30degree are acute angles such that sin theta=cos(3theta-30degree), then find the value of tan theta

Answer 1

Given:
sinθ = cos (3θ-30)

We know that cos (90-θ) = sinθ
Using this,
cos (90-θ) = cos (3θ-30)

Since there is cos on both sides,
90-θ = 3θ-30
4θ = 120
θ = 30°

tanθ = tan30 = $1/ \sqrt{3}$

Hope this helps!

Answer 2

Answer:

Step-by-step explanation :

GIVEN : sinteta = cos (3 teta- 30°)

Teta and 3teta -30° are acute angle

Prove: value of teta

Proof : cos (90°- teta) = cos (3teta- 30°)

90°-teta = 3teta - 30°

90°+30°=3teta+ teta

120°= 4teta

120/4= teta

30°= teta

Hence proved

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